We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum of a countable stable theory and, additionally, that simple unstable theories have PC-exact saturation at singular cardinals (...) satisfying mild set-theoretic hypotheses. This had previously been open even for the random graph. We characterize supersimplicity of countable theories in terms of having PC-exact saturation at singular cardinals of countable cofinality. We also consider the local analog of PC-exact saturation, showing that local PC-exact saturation for singular cardinals of countable cofinality characterizes supershort theories. (shrink)

A theory [Formula: see text] is said to have exact saturation at a singular cardinal [Formula: see text] if it has a [Formula: see text]-saturated model which is not [Formula: see text]-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.

We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give criteria for a theory to have singular compactness.

This article aims to explore the philosophical approach to faith after deconstruction as manifested in the work of Jean-Luc Marion and Jean-Luc Nancy. By taking the saturated phenomenon as its focus, the analysis seeks to demonstrate that whilst Marion’s thinking proves to be an innovative re-imagining of the possibilities of phenomenology, its problematic recourse to a supplementary hermeneutic means that saturation can never be adequately applied to faith without simultaneously compromising the excessive intuition upon which it relies. The article (...) then explores whether Nancy’s suggestion that saturation be re-framed as faith can offer a viable alternative approach. Whilst the post-phenomenological modality within which Nancy operates means it may be problematic to retain the term ‘saturation’ in the exact sense Marion gives it, it is argued that Nancy’s version of saturated faith allows us to approach the binary divide between philosophy and theology from a different direction, resulting in a vision of faith that cuts across theism and atheism, destabilising them from within. Although Nancy’s thought in this area certainly does nothing to respond to persistent questions surrounding the place of institutionalized religion within secular modernity, it nevertheless serves as a powerful tool for thinking the possibilities of faith in the twenty-first century. (shrink)

A model of Peano Arithmetic is short recursively saturated if it realizes all its bounded finitely realized recursive types. Short recursively saturated models of $\PA$ are exactly the elementary initial segments of recursively saturated models of $\PA$. In this paper, we survey and prove results on short recursively saturated models of $\PA$ and their automorphisms. In particular, we investigate a certain subgroup of the automorphism group of such models. This subgroup, denoted $G|_{M(a)}$, contains all the automorphisms of a countable short (...) recursively saturated model of which can be extended to an automorphism of the countable recursively saturated elementary end extension of the model. (shrink)

In this paper we investigate the properties of automorphism groups of countable short recursively saturated models of arithmetic. In particular, we show that Kaye's Theorem concerning the closed normal subgroups of automorphism groups of countable recursively saturated models of arithmetic applies to automorphism groups of countable short recursively saturated models as well. That is, the closed normal subgroups of the automorphism group of a countable short recursively saturated model of PA are exactly the stabilizers of the invariant cuts of the (...) model which are closed under exponentiation. This Galois correspondence is used to show that there are countable short recursively saturated models of arithmetic whose automorphism groups are not isomorphic as topological groups. Moreover, we show that the automorphism groups of countable short arithmetically saturated models of PA are not topologically isomorphic to the automorphism groups of countable short recursively saturated models of PA which are not short arithmetically saturated. (shrink)

Recanati takes for granted the conveyance conception of linguistic communica- tion, although it is not very clear exactly where he lies on the spectrum of possible variations. Even if we disavow all such conceptions of linguistic communication, there will be a place for semantic theory in articulating normative concepts such as logical consistency and logical validity. An approach to semantics focused on such normative concepts is illustrated using the example of ““It’’s raining””. It is argued that Recanati’’s conception of semantics (...) as involving the pragmatics of saturation and modulation cannot account for the logical properties of ““It’’s raining”. (shrink)

In an ω1-saturated nonstandard universe a cut is an initial segment of the hyperintegers which is closed under addition. Keisler and Leth in [KL] introduced, for each given cut U, a corresponding U-topology on the hyperintegers by letting O be U-open if for any x ∈ O there is a y greater than all the elements in U such that the interval $\lbrack x - y, x + y\rbrack \subseteq O$ . Let U be a cut in a hyperfinite time (...) line H, which is a hyperfinite initial segment of the hyperintegers. The U-monad topology of H is the quotient topology of the U-topological space H modulo U. In this paper we answer a question of Keisler and Leth about the U-monad topologies by showing that when H is κ-saturated and has cardinality κ, (1) if the coinitiality of U1 is uncountable, then the U1-monad topology and the U2-monad topology are homeomorphic iff both U1 and U2 have the same coinitiality; and (2) H can produce exactly three different U-monad topologies (up to homeomorphism) for those U's with countable coinitiality. As a corollary H can produce exactly four different U-monad topologies if the cardinality of H is ω1. (shrink)

Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the first order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use the machinery of neither saturated models nor elementary (...) chains. (shrink)

The appearance of negative terms in quasiprobability representations of quantum theory is known to be inevitable, and, due to its equivalence with the onset of contextuality, of central interest in quantum computation and information. Until recently, however, nothing has been known about how much negativity is necessary in a quasiprobability representation. Zhu :120404, 2016) proved that the upper and lower bounds with respect to one type of negativity measure are saturated by quasiprobability representations which are in one-to-one correspondence with the (...) elusive symmetric informationally complete quantum measurements. We define a family of negativity measures which includes Zhu’s as a special case and consider another member of the family which we call “sum negativity.” We prove a sufficient condition for local maxima in sum negativity and find exact global maxima in dimensions 3 and 4. Notably, we find that Zhu’s result on the SICs does not generally extend to sum negativity, although the analogous result does hold in dimension 4. Finally, the Hoggar lines in dimension 8 make an appearance in a conjecture on sum negativity. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

By recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal "infinitesimal subgroup" G00 such that the quotient G/G00, equipped with the "logic topology", is a compact (real) Lie group. Our first result is that the functor G → G/G00 sends exact sequences of definably compact groups into exact sequences of Lie groups. We then study the connections between the Lie group G/G00 and the (...) o-minimal spectrum G̃ of G. We prove that G/G00 is a topological quotient of G̃. We thus obtain a natural homomorphism ψ* from the cohomology of G/G00 to the (Čech-)cohomology of G̃. We show that if G00 satisfies a suitable contractibility conjecture then $\widetilde{G^{00}}$ is acyclic in Čech cohomology and ψ* is an isomorphism. Finally we prove the conjecture in some special cases. (shrink)

We show that for every countable recursively saturated model M of Peano arithmetic and every subset A⊆M, there exists a full satisfaction class SA⊆M2 such that A is definable in (M,SA) without parameters. It follows that in every such model, there exists a full satisfaction class which makes every element definable, and thus the expanded model is minimal and rigid. On the other hand, as observed by Roman Kossak, for every full satisfaction class S there are two elements which have (...) the same arithmetical type, but exactly one of them is in S. In particular, the automorphism group of a model expanded with a satisfaction class is never equal to the automorphism group of the original model. The analogue of the first result proved here for full satisfaction classes was obtained also by Roman Kossak for partial inductive satisfaction classes. However, the proof relied on the induction scheme in a crucial way, so recapturing the result in the setting of full satisfaction classes requires quite different arguments. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The TripletsManeesh BatraI am a neonatologist and for the majority of my clinical time I care for babies and their families at a large University-based referral neonatal intensive care unit (NICU) in the United States. In 2003, I first visited this rural Ugandan hospital shortly after the opening of a special care baby nursery there, and have been involved with development of that program ever since.Uganda is a beautiful, (...) land-locked country in East Africa with a sordid political history. It is a developing country that is poor, mostly rural with a high fertility rate and a life expectancy of 42 years. The government spends $5 per capita per year on healthcare. The district with the hospital has a population of 500,000, the majority of which is rural. Access to health services is poor, even by Ugandan standards, and child mortality is in the higher band in the country.Most people in the region live in extended family clans. A common home is made of earth, with a grass roof, and a jerry can out front for collecting water from the well. It is an exquisitely lush landscape with fecund soil. At the hospital, there is limited electricity, lab support, medications, blood supplies, and health care workers. For the 200 bed hospital (that accommodates upwards of 400 inpatients when necessary, no one is turned away) there are four to seven Ugandan doctors, who do everything from C-sections, to colostomies, to HIV care to resuscitate babies in the NICU. For a ward of 20-80 patients there are one to two nurses, and maybe a nursing aide. Families do the majority of the care in the hospital, even in the NICU. Mum's express breast milk, perform tube feeds, wash the linens, notify staff when an IV infiltrates, and keep babies warm.Day OneAnother beautiful morning, with fresh instant coffee in hand, birds chirping and kids playing outside. It is good to be back. Over the last eight years, I've [End Page 78] made some close friends here and its good to be among them again. Every time I visit and return home, I leave a piece of me here, and bring back something new with me. This morning that feeling is overwhelming me, an incredible inspiration swells. I am not tired and I want to be busy. It is no wonder that this is where I was inspired to pursue caring for babies as my career. Over these years, it has been amazing to see the staff care for the community's babies and mums here. As an outsider, an opinioned one at that, I feel burdened at the thought of these babies dying somewhat needlessly. Is it really no-one's fault? How should one act in the face of scarcity, knowing there is a better standard to be had if only circumstances were different?I walked into the NICU to find triplets had arrived! Born at about 33 weeks they were two months early. Since they weighed around 1.5kg (about 3 lbs) each, they were at very high risk of dying —however, it was absolutely incredible to see the way they were tucked in by the skilled team. Within an hour of delivery—they were in incubators with IVs, having their hypoglycemia corrected, and two out of three were on oxygen (all of them had their O2 saturations checked). The three babies were tucked in so calmly, with the finest skill and expertise neonatal care anywhere has to offer. In stark contrast to the first admissions I witnessed years ago, the nurses now knew exactly what to do and how to do it. As a result, they had saved many lives and restored hope among the mums of the region that there was somewhere to go to get help. This success resulted in a healthy swagger among the staff because they could intervene successfully.These were spontaneous triplets to this young mum, who already had three other children. She looked tired when she walked into the NICU one hour (yes one hour) after delivering the trio, but if I hadn't known prior, there was no way to know... (shrink)

We use a fundamental theorem of Vaught, called the covering theorem in [V] (cf. theorem 0.1 below) as well as a generalization of it (cf. Theorem $0.1^\ast$ below) to derive several known and a few new results related to the logic $L_{\omega_1\omega}$. Among others, we prove that if every countable model in a $PC_{\omega_1\omega}$ class has only countably many automorphisms, then the class has either $\leq\aleph_0$ or exactly $2^{\aleph_0}$ nonisomorphic countable members (cf. Theorem $4.3^\ast$) and that the class of countable (...) saturated structures of a sufficiently large countable similarity type is not $PC_{\omega_1\omega}$ among countable structures (cf. Theorem 5.2). We also give a simple proof of the Lachlan-Sacks theorem on bounds of Morley ranks ($\s 7$). (shrink)

Section 1 is devoted to the study of countable recursively saturated models with an automorphism moving every non-algebraic point. We show that every countable theory has such a model and exhibit necessary and sufficient conditions for the existence of automorphisms moving all non-algebraic points. Furthermore we show that there are many complete theories with the property that every countable recursively saturated model has such an automorphism. In Section 2 we apply our main theorem from Section 1 to models of Quine's (...) set theory New Foundations (NF) to answer an old consistency question. If NF is consistent, then it has a model in which the standard natural numbers are a definable subclass N of the model's set of internal natural numbers Nn. In addition, in this model the class of wellfounded sets is exactly $\bigcup_{n\in \mathbb{N}}\mathscr{P}^n(\varnothing)$. (shrink)

Since 2008 I have been closely following the conceptual/performance/video work of Daniel Peltz. Gently rendered through media installation, ethnographic, and performance strategies, Peltz’s work reverently and warmly engages the inner workings of social systems, leaving elegant rips and tears in any given socio/cultural quilt. He engages readymades (of social and media constructions) and uses what are identified as interruptionist/interventionist strategies to disrupt parts of an existing social system, thus allowing for something other to emerge. Like the stereoscope that requires two (...) identical images to create an illusion of a three-dimensional image, Peltz sometimes visualizes two separate elements to create an object or moment that requires space and depth to focus on its varied layers. They say your brain has to process and make meaningful sense out of all that visual information before it can accept the illusion. I say your brain has to do a similar thing when looking and seeing the divine, magical, and faithful (social) art making of Daniel Peltz. Daniel Peltz is Associate Professor of Film/Animation/Video at RISD. He divides his time between Rhode Island and Sweden and is currently at work on an exhibition at Botkyrka Konsthall, Stockholm opening February 2013 and a new project to be included in the IASKA: Spaced Biennial (Australia) in 2014. This interview took place on Skype and is part one of a two-part interview. Feliz Lucia Molina: Are you in Providence, RI? Daniel Peltz: I’m at my house in Providence. I’ve been back for six days teaching winter session at RISD and doing this workshop series—these investors’ drum circles with a group of wealth managers. a client of the firm, 2013, photo Shirin Adhami FLM: The wealth managers were all drumming together? DP: They were all drumming in response to the performance of their retirement portfolios. FLM: Is this part of the “Unrealized Gain/Loss” piece? DP: Yes, it’s part of a show I’m working on in Sweden. I can show you because it was just today. I’ll show you some of this. Lets see—share screen [click, click, click]. This is the room. I’ve been using the camera system that’s already installed in the conference rooms to record them. So the video is being recorded directly by the wealth management office’s tech staff. These are the people I worked with in the last workshop. This conference table is less wondrous. They’ve been learning to drum in response to their retirement portfolios. I started by bringing in my little bit of wealth for them to propose a management strategy, I came to the follow-up meeting with a counter proposal, which was this workshop. So they agreed to do this series of workshops instead of managing my wealth. FLM: Does everybody in the room manage your wealth? That’s kind of a lot of people. DP: That woman in the back there and Craig —they handle new client business. So when you come there with your wealth, they sit down with you and suggest to you how they would manage it. They’re very nice, responsible people. FLM: And where is this? DP: This is in Providence and the one I was showing you is in Waltham, where I was today. Then I’m going to Newport for the last one on Friday. So I will have done four of them. This is the group in Waltham that I just played with today. I played directly with the two groups in Providence and I’m working with an ethnomusicologist at Brown, Asha Tamarisa, who is facilitating the last two. She’s helped develop the workshop in terms of figuring out how to train a group to do this and thinking about the compositional challenges of working in response to retirement portfolio data. FLM: Screensharing helps me to figure out tiny bits here and there about the project. DP: I might even be able to play you a little of the audio I’ve also been working with a group of professional percussionists on what will become a quarterly public investors’ drum circle event. Their stuff was really nice, but I want you to hear what we sounded like in the workshops. They’ve all been recorded by the a/v system in the offices. We use a simple structure where the drummer investors interpret the sensation of gain or loss as embellishments to a base heartbeat rhythm. The group holds the heartbeat and, as each person experiences gain or loss, they embellish that rhythm. "Screensharing helps me to figure out tiny bits here and there about the project" FLM: Is the process all very spontaneous? DP: Its actually quite structured. We produce a custom stock ticker that shows the performance of their collective portfolios. In advance of the workshop each participant submits assets in their retirement portfolio. Then we make a stock ticker that shows the real-time performance of their assets so that they can respond to almost live data. FLM: Are they reading the stock ticker projected up on the screen in the room? Do people drum in correspondence to the visual live data of the performance of their assets? DP: Exactly. They’re looking at the stock ticker as opposed to each other, so it’s a slightly shifted drum circle. They’re looking at the ticker but they’re listening to each other—that’s what we’re practicing. For example, NVO—the price is 172.08 but it’s down -1.16 and as that moves across the screen, the person who’s retirement is invested in that asset starts to embellish when that arrow first appears, based on their experience of loss. They stop when it exits the screen and return to the heartbeat. You could have one ticker for each retirement portfolio, but the way the workshop is constructed is that we just isolate one asset from each person’s portfolio so that everyone in the group is represented in a single ticker. So they’re drumming and looking at the ticker, but they’re hearing each other experience gain and loss. We’ve removed direct visual engagement from the social structure of a drum circle but the oral engagement is still there. FLM: So they had their own sound interpretation of gain and loss? DP: Yeah and that part is quite spontaneous as you were saying. In some of the preparatory exercises we’ve been working to give the participants more strategies for interpreting the sensations of gain and loss. We’re trying to develop their capacity to embellish a heartbeat or base rhythm but I’m not invested in having a melodious result. I’m quite curious about what this kind of structure will result in without any desire for a particular result. FLM: For context, can you talk about the project you did a couple years ago in Bali, “Unrealized Gain/Loss” in relation to this current wealth management project? DP: The workshops I’ve been doing use a similar strategy to the other components in this project. It started in Indonesia on my sabbatical and I was really trying to understand where I was physically and where I was being on sabbatical—this kind of strange jubilee structure where every seventh year you’re supposed to renew your self. And it was around the time of the global financial crisis. I was on sabbatical for the global financial crisis. I remember watching my father, in particular, respond to the financial crisis by monitoring his retirement portfolio and trying to make sense of it. I realized on a visit to their home that he checked his retirement portfolio every single day and I was really struck by that because in some way our parents are mysteries to us as children, especially their moods. We know how important their moods are but we don’t know what governs them. And somehow it was like I’d figured it out, it’s the performance of the DOW! So I think there was something in that. Then I was in Indonesia and I had been drawn there by an interest in their highly ritualized Hindu culture, where so much of life is driven by a ceremonial calendar. I was interested in Bali as this predominantly Hindu pocket within a predominantly Islamic country and life there being organized by this ritual calendar functioning as a kind of resistance to the dominant global religion of free-market capitalism. So I started to explore that correlation between the ways in which this culture that I was living in was sort of “living for the afterlife” and this idea within certain segments of American society of “living for the afterwork life”. The idea that your wellbeing in the “afterwork life” is tied to forces that are unseen and largely beyond your control has strong similarities to many religious understandings of the universe. So I started to explore that and the crafts and materials that were around me were primarily Batik and percussion. Percussion is a huge part of daily life in Bali. These gamelan troupes were everywhere. And I also happened to be there for Nyepi, the day of silence, which is preceded by a very elaborate procession and construction of demonic statues. These were the things that were around me and I started studying Batik with one of the Batik artists there and also started a conversation with two master Batik artists, one who is American and her Indonesian husband. I developed these patterns that were based on symbols from the performance of my retirement portfolio and worked with the batik artists to produce two sarongs. d. peltz - 2012 In producing the designs, I treated the performance of my retirement portfolio since my arrival at RISD [7 years] as a significant interval and then I looked at the ways in which decisions are made within retirement portfolios as having an extension outwards from the individual assets that underlie the retirement portfolio, which are kind of like the base elements of the retirement world. Then there’s the allocation of your assets, which is a global way of understanding an individual according to typologies, which are often referred to in terms of risk—this notion of a ‘risk profile’. What type of ‘person’ you are is determined by your attitude towards risk, or potentiality, and I found that to be a really fascinating way of understanding the universe. I remember looking at the tabs in my retirement portfolio and finding this one for viewing ‘Unrealized Gain/Loss’ and that’s often how I work—is just going through the Cambridge Parking Code, for example, and finding this section of the code that was called ‘Crossing Non-Signalized Locations’ and just feeling “I can’t do any better than that,” you know? That’s what I was talking about in terms of ready-mades that exist in the social sphere. So I found that tab, actually, a long time ago, and I pulled it out of a journal when I was there [in Bali] working on these pieces and I wound up making these two sarongs and later on a series of porcelain vessels for holding one’s unrealized gains and losses. At the time, I knew that I wanted a performance to come out of them, but I wasn’t sure what it was. I was inspired very much by this sort of thing: Pulls out a TIAA-CREF brochure with a man in a suit seated at a table. This guy is probably an actor, and [the brochure] says “TIAA-Cref announces “Individual counseling sessions at the Rhode Island School of Design. Individual counseling sessions at no additional cost to you. You can discuss your personal financial situation with an experienced TIAA consultant on a confidential basis. We are available to help you discuss how to achieve your financial goals by investing in financial solutions such as mutual funds, brokerage, life insurance, and annuities...etc....What retirement benefits best fits your situation?” Often I encounter this and I think O.K., this is one way to prepare for the after-work life and it seems inadequate to me. But, I also find it really inspiring. I really like the visual language of it. I kind of want to be that man. I’d like to see if I could maybe buy his clothes. FLM: What it is about the man on the brochure that interests you? DP: He’s offering personalized objective advice and a detailed evaluation of everything you need to know and do. Who wouldn’t want that? But he’s also something of a contemporary priest or priestess, mediating between the unseen all-powerful universe of global capitalism and the common worker. So I started off developing Unrealized Gain/Loss directly from the charts that represent the performance of my retirement portfolio. Then I came home and I wanted to use those. I had this word in my journal “unrealized gain/loss vessel.” I had this notion of vessels that would contain unrealized gains and losses. That felt really important to me that they would have somewhere to go. I had been thinking a lot about altars and making offerings—that somehow this really fickle, massive, difficult-to-comprehend-universe of the financial world—that somehow it might be nice if you could making an offering to it. [In Bali] they made such beautiful elaborate offerings. So I studied offering making as well with one of the women there and she taught me some of the standard forms created by folding leaves and the significance of the floral arrangements. I started working in clay and then moved to porcelain and I made these unrealized gain/loss vessels. I made a few of them, they have holes on either side that you can’t get your fingers in. But something can go in there and something can go out of there. It’s a nice size for putting on an altar. Then I got this commission from Artists in Context who was interested in my doing something for this project “Artists Perspectives for the Nation” project. I proposed initiating these investors’ drum circles as a new public performance form. I’m interested in bringing together those two symbols—the symbol of the djembe and the drum circle. unrealized gain/loss vessel - d.peltz - 2012 FLM: I can imagine the public digital stock ticker performing like a soft fleeting stream of information, a kind of (meaningless) illusory comfort blanket. DP: In some way you have to understand its relevance outside of the obvious, right? Because the obvious is illogical. Nobody is actually using that data to day trade, for example. People aren’t sitting there with their computers watching the market data in Times Square or setting up an outdoor office and being like “OK it’s up 3 points or it’s up 1.56, trade! Ok now buy, Ok now sell!” That would be a kind of a nice performance, actually. But actual day traders would want more up to date data than that. To understand what that data is doing is really important. And that’s something I’ve realized—that I’m interested in a particular kind of data visualization, which is not about what data can tell people, but what data can tell people who are visualizing it. For example, in the Cambridge Project “Crossing Non-Signalized Locations” I was interested in the 10,000 excuses archive of data recording five years worth of excuses for why people thought they shouldn’t have received their parking ticket. I was not interested in making that excuse wall so that the public could see and understand this data. Inevitably the data will be seen by others but I was really interested in what the action of visualizing the data told those who were visualizing it. The parking attendants themselves were writing those excuses on the wall—I was interested in what that kind action of writing the excuses on the wall told them about the data. Similarly, I’m interested in designing a way to allow people to pass this data from the unseen universe of the market, through their own bodies, which happens through the merging of the drum and the stock ticker. I’m interested in those two also as symbols; the drum as this symbol of the earth, the body and a pagan counterculture, and the stock ticker referring to the ethereal world of global markets—bringing those two together and making them dependent. I’m often drawn to conceptual propositions that I become invested in testing in a sincere way—at first they often they sound humorous to others, but I have to remember that there is humor in them. I don’t sit around and laugh about these things. I stop finding them funny at all. I’m interested in the proposition that we could know something about the after-work life by drumming in response to our retirement portfolio. So then I become really interested in how to craft that into a viable performance form for myself and others. FLM: The aspect of using sound in “Unrealized Gain/Loss” as a way of embodying the information to the asset holder is really intriguing—using sound as a means of embodying the asset data. Was sound a medium that made sense to use immediately or were you considering other means of attempting to embody it? DP: Well I do use other mediums within the project like textile, ceramic, and batik patterns. I was first drawn to the history of Batik patterns as a socio-economic stratification system and the vessels as a way of embodying or manifesting this data of unrealized gain and loss. My first approach was to work with meditation actually—a meditation workshop with my colleagues. I was going to offer this “Unrealized Gain/Loss” workshop where you would explore the sensations of gain and loss by adapting the way yogi-nidra brings you into contact with your physical surroundings and stretches your perception. FLM: At Naropa University there are/were business & compassion workshops—a sort of mash-up of business and compassion and how compassion could be incorporated into a business model. This process and engagement of “embodying data” also has to do with “Participatory Democracy and the Future of Karaoke” you created at the DNC in Denver in 2008. DP: That kind of appropriation and instrumentalization of spiritual practice could be disturbing and thus compelling as a strategy. For various reasons, I’ve come to be drawn to both the form of a quarterly public performance and the established performance form of a drum circle. Its something I’ve seen myself do before, that is to mess up a really good functional social system like a drum circle or karaoke. I remember I was developing language for the karaoke project and started calling it “Participatory Democracy and the Future of Karaoke” and one of my assistants on the project, who’s an incredible artist, said, “but don’t you think the future of karaoke is guitar hero?” and I realized that maybe he thought I was trying to improve the form. I’m just trying to get people to have this shifted embodied experience, I need to craft the performance context so that they can do that. In the case of the karaoke project, for example, what did I need in order to be able to do this [a person to stand up in front of a bar and deliver a karaoke speech]? I realized that the body is very vulnerable so I built a podium so that the speaker can feel secure enough to do this, otherwise you couldn’t get to this state achieved by passing these speeches through the body. Then I was, like, well you need to be able to practice the lyrics because you don’t know all the “songs” by heart, which became an insert to the massive track books carried by most karaoke VJs. And then sometimes the crowd in the bar isn’t there with me, so I needed to extract the voice of the crowd cheering from the original venue and I needed the local audience to cheer if they wanted to. I’m interested in both where the form succeeds and fails. In particular, one of the most interesting things is this auditory gap between the space where you are, the reduced scale of applause in your own little bar, and this grand scale of applause at the convention center where the speech was originally delivered. FLM: How did the concept of “Participatory Democracy Karaoke” come about and why did you use karaoke as a means of engaging what was happening at the DNC in 2008? DP: I was looking at a lot of different readymade media infrastructures within the city at the time. I was interested in the emergency broadcast systems and I developed a proposal to repurpose that system and karaoke became an important symbol because it was this populist form that was already engaged in exploring the sensation of celebrity but also visualizing the gap between ourselves and those with more power and influence. So it had this readymade capacity to play with power and celebrity and I felt like the Obama presidential campaign, the first one in particular, had some very curious overlaps with this culture of celebrity. Obama of course rose to power partly based on his oratory abilities and I was interested in how karaoke as a vehicle was so adept at offering people all that was left of authentic expression in a political speech. Managing a politician and constructing their identity is such a developed practice that it becomes, kind of automatically, a metaphor for the way that our own identities are constructed. Of course the Obama campaign was very hip and savvy and deploying this notion of grassroots. It was really pioneering in its use of social media and this deployment of notions of populism. I was interested at that time in the capacity of karaoke to track speech patterns, precise tempos of anyone’s delivery, and that to me was a way of thinking about what might be left of the authentic self. I was interested in karaoke’s capacity to extract that authentic component and offer it to others. So not just to stand up and be them, but to [literally] pass their speech patterns through your own body. A long time ago, it started to strike me as odd that one would make media at all. It struck me as a kind of un-contemporary way of going about making art in an age of media overflow. That logic extended into my thinking on delivery devices and installation as well. Why would one buy a screen or even set one up when there are so many out there? And the way in which these media displays function in karaoke bars and bars in general is very interesting to me. I’m drawn to this passive consumption of media where your primary social interaction is with the bartender or a few other individuals but these screens are around you and your attention is shifting back and forth between these spaces. So much political rhetoric is spoken to a half-listening audience. I was interested in what was happening in the slippage and that karaoke was a kind of slippage amplifier. So if you put people in a bar and they are delivering a Kucinich speech and Kucinich comes up on a screen then your getting a sound bite of Kucinich and an image of Kucinich and your friend is talking to you— FLM: A kind of magic takes place in that incongruency between sound and image and the karaoke participant who’s relaying the speech-text at the same time. DP: Exactly and there’s some kind of truth in that experience of reality. FLM: Yeah, there’s something uncanny about seeing the body close-up like that as though it can’t lie to you in that moment or context. It’s a weird moment of luminous clarity. The work you’ve done and all of what you’re saying about karaoke is so very interesting to me. Growing up, my dad and uncles sang karaoke a lot (and still do) and being first-generation Filipino American is a different cultural subtext entirely. I’m also seeing it from the position of witnessing family members who are carriers of these stories and songs. And seeing them cherish these Tony Bennett, Frank Sinatra, Elvis Presley songs so much, I also see how their bodies are literal vessels of popular music that signifies something greater—it signifies their cultural and socioeconomic place in the world. The way that they cherish these American 1950s and 1960s pop songs is similar to having a certain kind of reverence for their spiritual faith or Catholicism. It’s a similar kind of care, focus, and attention exerted in karaoke and Catholicism—that these two structures and systems give something to focus on. Setsuko, Seiji and Hitoshi in Obama, Japan as Obama in Indiana — d. peltz — 2008 DP: Sure there something about the relationship we have to our candidate or the way we go about choosing a candidate, which is very similar to a deity or idol. I learned a lot about karaoke culture through this project. I’d never done karaoke. I’d never been interested in it as a form and then I travelled to Japan as part of the project when I made “Setsuko, Seiji and Hitoshi in Obama, Japan as Barack Obama in Indiana” and it was quite fascinating because my image of karaoke had always been this very public forum in a karaoke bar and then I discovered there’s this whole other world of karaoke where people even go on their own, they go and rent a room or cubicle and sing, or they go on a date—just the two of them go and sit in a room and do karaoke together. FLM: I’m interested in issues that take place within or as a result of specific karaoke culture(s). In the Philippines within the last several years there’s been occurring the “My Way Killings” phenomenon. Apparently baklas or gay men are employed by karaoke establishments to help “smooth over conflicts over karaoke singing”—these social forms of conduct, or lack thereof that arise out of the infrastructures of this social sport. In this one rural part of the Philippines there’s a village karaoke machine that the whole village shares—the Aeta indigenous people have an appointed “keeper” of the karaoke machine. I also see karaoke as a proxy to the confessional box in Catholicism where one goes to pour out their sins (minus the penance and redemption). The karaoke machine enables one to literally sing out whatever’s going on internally, but through highly saturated popular song lyrics. While karaoke is a public and social sport, it can also be a private one. Karaoke is a means of communion with each other. DP: Right, this preference for this kind of mediated communication. In Japan I was trying to organize people to work on this project and I was talking about throwing a party and they were like, well, we have to rent a karaoke machine because what else are we going to do? And I think its kind of serving that function of surrogacy—emotional surrogacy. FLM: And karaoke tools can be read as ritual tools—the magic mic that holds everything. There’s got to be some overlap at some point—between religious ceremony and devotion to the karaoke machine. DP: The way I designed the piece was so that it could slip right on top of the ready-made karaoke infrastructure. There was a flat-packed podium and it was made of a single sheet of plywood with no fasteners that slotted into itself. Those were sent out to a network of karaoke bars that I invited to become “karaoke convention centers.” The local VJs downloaded our custom-made, speech-extracted tracks that were designed to play on their existing equipment. In this sense the piece is a permanent installation. If you go to Denver today, some of the VJs still have the tracks in their library of offerings, the Ramones and Romney. It was this notion of re-purposing readymade infrastructure to create a distributable populist form. Obama was coming and the convention was in the Pepsi Center and 30,000 people were coming including 10,000 journalists. The impetus behind the larger art project that commissioned international artists to make works in Denver, was that local people weren’t going to have much access to this convention. It was like an invasion, the city was being descended upon, but if you lived a block away from the site, you had the same access as people in Zimbabwe&mash;30 second media bits excerpted from the speeches. So it seemed to me that the fundamental gesture was how do I take that signal, which was travelling out of the convention center, and create a local interruption? FLM: Is that what you mean by ‘intervention’? The term is frequently used to help describe your work. DP: It depends on the day. Around that karaoke project I had a conversation with Krzysztof Wodiczko and he was proposing that maybe rather than intervention, we should consider the word interruption. Because intervention is kind of an overused term in the field of art and it has militaristic and therapeutic associations outside of the art context. Fundamentally, the idea of intervening speaks to the readymade social world as your primary material. So it’s basically suggesting a kind of subtractive process, which gets back to this question: what is the role of the contemporary media artist in a world that’s so saturated with media? You can’t work additively in a saturated field. If you want to make a visible mark you have to work subtractively. That’s what intervention is about to me, just another way of saying “to work subtractively.” FLM: So the interventions or interruptions aren’t necessarily adding or subtracting, but are they putting orange cones there? What are they doing exactly? DP: I think you’re right about that, they’re not really subtracting. They’re adding to the scope of possibility. I’ve been thinking (with this exhibition I’m mounting next month) about the work as explorations and expansions of social possibility. Maybe it’s more insertion. I started calling the pieces ‘insertions’ that I was making in Rejmyre—a small town in Sweden where I’ve been working for six years now. My favorite site to install there is the tourist bureau. I started calling the video pieces that I made for the tourist bureau, video insertions. This idea that you’re inserting something into the readymade media infrastructure of the world resonates with me. Insertion leverages a context, creating a possibility that the inserted object might be naturalized in the process — that someone can encounter my video in Rejmyre as tourist information. And then all of a sudden tourist information can include some American guy prostrating through town and it can include really bad relationship advice. Maybe insertion is a better word. tourist information – d. peltz 2009-present  . (shrink)

The challenges with modeling the spread of Covid-19 are its power-type growth during the middle stages of the waves with the exponents depending on time, and that the saturation of the waves is mainly due to the protective measures and other restriction mechanisms working in the same direction. The two-phase solution we propose for modeling the total number of detected cases of Covid-19 describes the actual curves for many its waves and in many countries almost with the accuracy of (...) physics laws. Bessel functions play the key role in our approach. The differential equations we obtain are of universal type and can be used in behavioral psychology, invasion ecology (transient processes), etc. The initial transmission rate and the intensity of the restriction mechanisms are the key parameters. This theory provides a convincing explanation of the surprising uniformity of the Covid-19 waves in many places, and can be used for forecasting the epidemic spread. For instance, the early projections for the 3rd wave in the USA appeared sufficiently exact. The Delta-waves (2021) in India, South Africa, UK, and the Netherlands are discussed at the end. (shrink)

Based on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a nonlinear pulse term depending (...) on the density of real-time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order-1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state-dependent feedback control models. (shrink)

Khoussainov and Nerode [14] posed various open questions on model-theoretic properties of automatic structures. In this work we answer some of these questions by showing the following results: There is an uncountably categorical but not countably categorical theory for which only the prime model is automatic; There are complete theories with exactly 3,4,5,…3,4,5,… countable models, respectively, and every countable model is automatic; There is a complete theory for which exactly 2 models have an automatic presentation; If LOGSPACE=PLOGSPACE=P then there is (...) an uncountably categorical but not countably categorical theory for which the prime model does not have an automatic presentation but all the other countable models are automatic; There is a complete theory with countably many countable models for which the saturated model has an automatic presentation but the prime model does not have one. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Promise of Martin Luther's Political Theology: Freeing Luther from the Modern Political Narrative by Michael Richard LaffinCandace L. KohliThe Promise of Martin Luther's Political Theology: Freeing Luther from the Modern Political Narrative Michael Richard Laffin NEW YORK: BLOOMSBURY / T&T CLARK, 2016. 272 pp. $121.00Is Christianity antagonistic of the political, as Machiavelli, Rousseau, and Nietzsche have all claimed? Michael Laffin argues against this position for "the life-affirming, (...) this worldliness of Christianity" by pointing to the "theologically saturated politics of [Martin] Luther" as one historical possibility (4). In particular, Laffin elevates Luther's notion of the three estates, the locus of sanctification in Luther's thought, and the Reformer's doctrine of the "two ecclesiae" as concepts holding together the "this-worldly" dimension of life with the theological tension of the fall and redemption. In this way, Laffin identifies a truly political life lived in community and a thoroughly theological politics extending from faith in the justifying God (3). Laffin defends Luther against charges of violent individualism (contra John Milbank) and quietism (contra [End Page 202] Jennifer Herdt) by highlighting the importance of the theology of the Word for Luther's treatment of politia. Per Laffin, Luther understands the Word as Christ's radically incarnate presence that transforms this-worldly communities by sanctifying the Christian's affections, which are then lived out in political relationships (chaps. 1–3). The politia therefore becomes a place of encounter with God in which the re-created human heart commits acts of moral beauty that are distinctively Christian (chaps. 4–5).One strength of Laffin's argument is his thoroughgoing critique of the constructed narratives in contemporary political theology and philosophy that construe Luther as the harbinger of modernity's ills, as the inventor of the desocialized individual via his notion of faith and a proponent of quietistic authoritarianism in his elevation of human passivity in justification. By looking outside Luther's classic "political" texts, Laffin shows that careful study of Luther's broader writings on scripture, the sacraments, and ecclesiology actually reveal complex theological theories about the place of the political in realizing the good in human life and community. Both Laffin's critique of Milbank's ontology of violence and his assertion about human moral agency in the politia presuppose, however, that Luther's theological move from justification to sanctification includes the possibility for some kind of real, effectual change in the human person. This requires a metaphysical language capable of describing ontological change, something Laffin negates when he denies Luther's creative reliance on nominalism (39). Laffin wants to assume this ontological change that makes human moral agency possible but restricts himself from engaging the historical realities of Luther's intellectual life that make his assumptions plausible. Laffin's deft critique of Milbanks and Herdt would be strengthened by a more nuanced understanding of Luther's simultaneous critique and use of nominalist theology and philosophy for contemplating human action in both divine and political relations. Here real possibilities exist for showing how Luther used nominalist principles to construct a view of human moral agency for political relationships through the theological locus of sanctification (contra Herdt) by rehabilitating human persons in relation to God (contra Milbanks).Despite this critique, Laffin's book opens up new questions about the historical narratives surrounding the secularization thesis and exactly what we mean by "political theology." Advanced political philosophers, theologians, and Christian ethicists must now reckon with the possibilities he creates for rethinking Luther's place in this narrative and the Reformer's ongoing relevance in current discussions. Laffin prompts these audiences to reconsider the extent to which the political and the theological can and do hold each other in tension, as he shows that Luther does. [End Page 203]Candace L. KohliNorthwestern UniversityCopyright © 2018 Society of Christian Ethics... (shrink)

A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

Individuals suffering from depression consistently report experiencing a lack of connectedness with others. David Karp (2017, 73), in his memoir and study of depression, has gone so far to describe depression as “an illness of isolation, a disease of disconnectedness”. It has become common, in phenomenological circles, to attribute this social impairment to the depressed individual experiencing their body as corporealized, acting as a barrier between them and the world around them (Fuchs 2005, 2016). In this paper, I offer an (...) alternative view of the experience of social disconnectedness in depression, suggesting that rather than necessarily experiencing their body as object-like, the depressed individual’s bodily is saturated with experiences of lethargy, tiredness, heaviness, sadness, hopelessness and so on, to the exclusion of being able to bodily connect to others. I suggest that depression does not involve a complete social impairment but a specific impairment of affective forms of interpersonal experience. (shrink)

This paper is devoted to the problem of existence of saturated models for first-order many-valued logics. We consider a general notion of type as pairs of sets of formulas in one free variable that express properties that an element of a model should, respectively, satisfy and falsify. By means of an elementary chains construction, we prove that each model can be elementarily extended to a $\kappa $-saturated model, i.e. a model where as many types as possible are realized. In order (...) to prove this theorem we obtain, as by-products, some results on tableaux and their consistency and satisfiability and a generalization of the Tarski–Vaught theorem on unions of elementary chains. Finally, we provide a structural characterization of $\kappa $-saturation in terms of the completion of a diagram representing a certain configuration of models and mappings. (shrink)

We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no ideal on Pκ is weakly λ+-saturated. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Saturated models constitute one of the powerful methods of conventional model theory, with many applications. Here we develop a categorical abstract model theoretic approach to saturated models within the theory of institutions. The most important consequence is that the method of saturated models becomes thus available to a multitude of logical systems from logic or from computing science. In this paper we define the concept of saturated model at an abstract institution-independent level and develop the fundamental existence and uniqueness theorems. (...) As an application we prove a general institution-independent version of the Keisler–Shelah isomorphism theorem “any two elementarily equivalent models have isomorphic ultrapowers” (assuming Generalized Continuum Hypothesis). (shrink)

Theorem 0.1LetK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}be an abstract elementary class with amalgamation and no maximal models. Letλ>LS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda > {LS}$$\end{document}. IfK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}is categorical inλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, then the model of cardinalityλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}is Galois-saturated.This answers a question asked independently by Baldwin and (...) Shelah. We deduce several corollaries: K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document} has a unique limit model in each cardinal below λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document} is weakly tame below λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, and the thresholds of several existing categoricity transfers can be improved.We also prove a downward transfer of solvability :Corollary 0.2LetK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}be an AEC with amalgamation and no maximal models. Letλ>μ>LS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda> \mu > {LS}$$\end{document}. IfK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}is solvable inλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, thenK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}is solvable inμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}. (shrink)

We put in print a classical result that states that for most purposes, there is no harm in assuming the existence of saturated models in model theory. The presentation is aimed for model theorists with only basic knowledge of axiomatic set theory.

We use the language of categorical logic to construct generic saturated models of intuitionistic theories. Our main technique is the thorough study of the filter construction on categories with finite limits, which is the completion of subobject lattices under filtered meets. When restricted to coherent or Heyting categories, classifying categories of intuitionistic first-order theories, the resulting categories are filtered meet coherent categories, coherent categories with complete subobject lattices such that both finite disjunctions and existential quantification distribute over filtered meets. Such (...) categories naturally embed into Grothendieck toposes which then contain saturated models of the theory we started with. (shrink)

Multiple-universe theories (involving the saturation of a state space of alternative universes) enjoy growing popularity as proposed counters to the design-suggestiveness of increasingly impressive cosmic fine-tuning cases. In this paper I explore this type of counter, and argue that (i) multiple-universe theoriesdo not necessarily undercut the design relevance of cosmic fine-tuning, that (ii) both the required saturation and the hypothesized mechanisms supposed to generate such saturation face seriously non-trivial constraints, and that (iii) in some cases the specific (...) characteristics of such saturations may themselves be suggestive of design. (shrink)

Given a regular uncountable cardinal κ and a cardinal λ > κ of cofinality ω, we show that the restriction of the non-stationary ideal on Pκ to the set of all a with equation image is not λ++-saturated . We actually prove the stronger result that there is equation image with |Q| = λ++ such that A∩B is a non-cofinal subset of Pκ for any two distinct members A, B of Q, where NGκ, λ denotes the game ideal on Pκ. (...) We also remark that for κ > ω1, adding λ+3 Cohen subsets of ω1 to equation image makes NGκ, λ λ+3-saturated. (shrink)

ABSTRACT The question of this article is whether the saturated phenomenon as articulated in the early work of Jean-Luc Marion may appear within language and history, or in other words how a non- or extra-horizonal event can appear within the horizons necessary for communication and communality. This problem is significant, among other reasons, because saturated aesthetic, ethical, and religious phenomena constitute important bases for communal values. The article argues that Hans-Georg Gadamer’s philosophy of language offers resources that allow us to (...) understand how a saturated phenomenon can appear communicably and communally without sacrificing the irreducible excessiveness of its appearance. The author draws on parallels between Marion and Gadamer to argue that the poetic word and the conversation present possibilities of the saturated phenomenon occurring within language and history, and suggests the “saturated question” as a name for this mode of appearance. (shrink)

The paper is a continuation of the investigations of [3]. We assume that the reader is familiar with the notion of an !-saturated model and the notation applied in the theory of models. We refer to [2] for all model- theoretic terms which appear in this note.

We show that under the assumption of the existence of the canonical inner model with one Woodin cardinal$M_1$, there is a model of$\mathsf {ZFC}$in which$\mbox {NS}_{\omega _{1}}$is$\aleph _2$-saturated and${\Delta }_{1}$-definable with$\omega _1$as a parameter which answers a question of S. D. Friedman and L. Wu. We also show that starting from an arbitrary universe with a Woodin cardinal, there is a model with$\mbox {NS}_{\omega _{1}}$saturated and${\Delta }_{1}$-definable with a ladder system$\vec {C}$and a full Suslin treeTas parameters. Both results rely on (...) a new coding technique whose presentation is the main goal of this article. (shrink)

$\underline{\text{Saturation is} (\mu, \kappa)-\text{transferable in} T}$ if and only if there is an expansion T 1 of T with ∣ T 1 ∣ = ∣ T ∣ such that if M is a μ-saturated model of T 1 and ∣ M ∣ ≥ κ then the reduct M ∣ L(T) is κ-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is (ℵ 0 , λ)- transferable or (κ (T), λ)-transferable for (...) all λ. Further if for some $\mu \geq \mid T \mid, 2^\mu > \mu^+$ , stability is equivalent to for all μ ≥ ∣ T ∣, saturation is (μ, 2 μ )- transferable. (shrink)

This book contains the material for a first course in pure model theory with applications to differentially closed fields.

A key topic within the field of the phenomenology of medicine has been the relationship between body and self in illness, including discussions about the otherness and mineness of the body. The aim of this article is to distinguish between different meanings of bodily otherness and mineness in illness with reference to the interpretation of the body as “saturated phenomenon,” inspired by the phenomenology of Jean-Luc Marion. With the help of Marion’s ideas it is possible to distinguish between two meanings (...) of bodily otherness and of mineness (objective and non-objective forms). These distinctions support and elaborate on ideas already found in the phenomenology of medicine and offer further insights into the nature of the experience of illness. (shrink)

The paper presents an outline of the general theory of countable arithmetically saturated models of PA and some of its applications. We consider questions concerning the automorphism group of a countable recursively saturated model of PA. We prove new results concerning fixed point sets, open subgroups, and the cofinality of the automorphism group. We also prove that the standard system of a countable arithmetically saturated model of PA is determined by the lattice of its elementary substructures.

Poorly saturated colors are closer to a pure grey than strongly saturated ones and, therefore, appear less “colorful”. Color saturation is effectively manipulated in the visual arts for balancing conflicting sensations and moods and for inducing the perception of relative distance in the pictorial plane. While perceptual science has proven quite clearly that the luminance contrast of any hue acts as a self-sufficient cue to relative depth in visual images, the role of color saturation in such figure-ground organization (...) has remained unclear. We presented configurations of colored inducers on grey ‘test’ backgrounds to human observers. Luminance and saturation of the inducers was uniform on each trial, but varied across trials. We ran two separate experimental tasks. In the relative background brightness task, perceptual judgments indicated whether the apparent brightness of the grey test background contrasted with, assimilated to, or appeared equal (no effect) to that of a comparison background with the same luminance contrast. Contrast polarity and its interaction with color saturation affected response proportions for contrast, assimilation and no effect. In the figure-ground task, perceptual judgments indicated whether the inducers appeared to lie in front of, behind, or in the same depth with the background. Strongly saturated inducers produced significantly larger proportions of foreground effects indicating that these inducers stand out as figure against the background. Weakly saturated inducers produced significantly larger proportions of background effects, indicating that these inducers are perceived as lying behind the backgrounds. We infer that color saturation modulates figure-ground organization, both directly by determining relative inducer depth, and indirectly, and in interaction with contrast polarity, by affecting apparent background brightness. The results point towards a hitherto undocumented functional role of color saturation in the genesis of form, and in particular figure-ground percepts in the absence of chromatostereopsis. (shrink)

$\underline{\text{Saturation is} -\text{transferable in} T}$ if and only if there is an expansion T$_1$ of T with $\mid T_1 \mid$ = $\mid T \mid$ such that if M is a $\mu$-saturated model of T$_1$ and $\mid M \mid \geq \kappa$ then the reduct M $\mid L$ is $\kappa$-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is - transferable or, \lambda$)-transferable for all $\lambda$. Further if for some $\mu \geq \mid (...) T \mid, 2^\mu > \mu^+$, stability is equivalent to for all $\mu \geq \mid T \mid$, saturation is - transferable. (shrink)

Suppose that λ is the successor of a singular cardinal μ whose cofinality is an uncountable cardinal κ. We give a sufficient condition that the club filter of λ concentrating on the points of cofinality κ is not λ+-saturated.1 The condition is phrased in terms of a notion that we call weak reflection. We discuss various properties of weak reflection. We introduce a weak version of the ♣-principle, which we call ♣*−, and show that if it holds on a stationary (...) subset S of λ, then no normal filter on S is λ+-saturated. Under the above assumptions, ♣*− is true for any stationary subset S of λ which does not contain points of cofinality κ. For stationary sets S which concentrate on points of cofinality κ, we show that ♣*− holds modulo an ideal obtained through the weak reflection. (shrink)

We study reducts of Peano arithmetic for which conditions of saturation imply the corresponding conditions for the whole model. It is shown that very weak reducts (like pure order) have such a property for κ-saturation in every κ ≥ ω 1 . In contrast, other reducts do the job for ω and not for $\kappa > \omega_1$ . This solves negatively a conjecture of Chang.

We show, using a variation of Woodin’s partial order ℙ max , that it is possible to destroy the saturation of the nonstationary ideal on ω 1 by forcing with a Suslin tree. On the other hand, Suslin trees typcially preserve saturation in extensions by ℙ max variations where one does not try to arrange it otherwise. In the last section, we show that it is possible to have a nonmeager set of reals of size ℵ1, saturation (...) of the nonstationary ideal, and no weakly Lusin sequences, answering a question of Shelah and Zapletal. (shrink)

We study the two model-theoretic concepts of weak saturation and weak amalgamation property in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly saturated objects of an accessible category ${\cal K}$. We discuss the implications of this fact in classical model theory.

In Reasons and Persons, Parfit (1984) posed a challenge: provide a satisfying normative account that solves the Non-Identity Problem, avoids the Repugnant and Absurd Conclusions, and solves the Mere-Addition Paradox. In response, some have suggested that we look toward person-affecting views of morality for a solution. But the person-affecting views that have been offered so far have been unable to satisfy Parfit's four requirements, and these views have been subject to a number of independent complaints. This paper describes a person-affecting (...) account which meets Parfit's challenge. The account satisfies Parfit's four requirements, and avoids many of the criticisms that have been raised against person-affecting views. (shrink)

Our aim was to try to generalize some theorems about the saturation of ultrapowers to reduced powers. Naturally, we deal with saturation for types consisting of atomic formulas. We succeed to generalize “the theory of dense linear order (or T with the strict order property) is maximal and so is any which is SOP3”, (where Δ consists of atomic or conjunction of atomic formulas). However, the theorem on “it is enough to deal with symmetric pre‐cuts” (so the theorem) (...) cannot be generalized in this case. Similarly the uniqueness of the dual cofinality fails in this context. (shrink)

We show that is a quasi-minimal torsion-free divisible abelian group. After discussing the axiomatization of the theory of this structure, we present its ω-saturated quasi-minimal model.