We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0 3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).

In this paper, the notion of the radical of a filter in BL-algebras is defined and several characterizations of the radical of a filter are given. Also we prove that A/F is an MV-algebra if and only if Ds ⊆ F. After that we define the notion of semi maximal filter in BL-algebras and we state and prove some theorems which determine the relationship between this notion and the other types of filters of a BL-algebra. Moreover, (...) we prove that A/F is a semi simple BL-algebra if and only if F is a semi maximal filter of A. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

It is shown that in ZF set theory the axiom of choice holds iff every non empty topological space has a maximal closed filter.

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing (...) complete. We obtain the reverse mathematics result that the principle "every countable poset has a maximal filter" is equivalent to ACA₀ over RCA₀. An unbounded filter is a filter which achieves each of its lower bounds in the poset. We show that every computable poset has a \Sigma^0_1 unbounded filter, and there is a computable poset with no \Pi^0_1 unbounded filter. We show that there is a computable poset on which every unbounded filter is Turing complete, and the principle "every countable poset has an unbounded filter" is equivalent to ACA₀ over RCA₀. We obtain additional reverse mathematics results related to extending arbitrary filters to unbounded filters and forming the upward closures of subsets of computable posets. (shrink)

Two countable filters on $\omega$ are incompatible if they have no common infinite pseudointersection. Letting $\alpha(P_f)$ denote the minimal size of a maximal uncountable family of pairwise incompatible countable filters on $\omega$, we prove the consistency of t $< \alpha(P_f)$.

I argue that classical counterfactual semantics in the style of Stalnaker, Lewis, and Kratzer validates an inference pattern that is disconfirmed in natural language. The solution is to alter the algorithm we use to handle inconsistency in premise sets: rather than checking all maximally consistent fragments of a premise sets, as in Krazter’s semantics, we selectively remove some of the premises. The proposed implementation starts from standard premise semantics and involves a new ‘filtering’ operation that achieves just this removal. The (...) resulting semantics is interestingly related to the semantics for counterfactuals emerging from Judea Pearl’s causal models framework in computer science: in particular, filtering is a possible worlds semantics counterpart of Pearl’s interventions. (shrink)

Two countable filters on ω are incompatible if they have no common infinite pseudointersection. Letting α(P f ) denote the minimal size of a maximal uncountable family of pairwise incompatible countable filters on ω, we prove the consistency of t $.

We introduce the property “F-linked” of subsets of posets for a given free filter F on the natural numbers, and define the properties “μ-F-linked” and “θ-F-Knaster” for posets in a natural way. We show that θ-F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. Concerning iterations of such posets, we develop a general technique to construct θ-Fr-Knaster posets (where Fr is the Frechet ideal) via matrix iterations of <θ-ultrafilter-linked posets (restricted to some level (...) of the matrix). This is applied to prove consistency results about Cichoń's diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal invariants associated with it are pairwise different. At the end, we show that three strongly compact cardinals are enough to force that Cichoń's diagram can be separated into 10 different values. (shrink)

For each integer n ≥ 2, MVn denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MVn are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MVn are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV3, the mentioned characterization of maximal subalgebras of A can be given (...) in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro. (shrink)

For each integer n ≥ 2, MVn denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MVn are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MVn are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV3, the mentioned characterization of maximal subalgebras of A can be given (...) in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro. (shrink)

There is a systemic condition inherent in contemporary markets that compel managers not to pursue more morally preferable initiatives if those initiatives will require actions that conflict with profit maximization. Normative arguments for implementing morally preferable practices within the existing system fail because they are insufficient to counter-act the systemic conditions affecting decision-making that is focused on maximizing profit as the primary operational value. To overcome this constraint we must elevate a more normatively preferable value, ‚ideal environmental sustainability,’ to the (...) level of being the primary filtering value through which other competing values are evaluated, prioritized, and implemented. In order for this to occur in practice, a change must be made relative to the laws, rules, and regulations that define and guide the market. This can be done by suitably defining the epistemic constraint of impartiality utilizing Rawls’ notion of a ‚veil of ignorance’ as a heuristic device. (shrink)

This paper is one of several contributions in a series, illustrating the application of a specific deductive methodology to explain diversity of form. The methodology facilitates the explanation of feeding morphologies in various ducks as a transformation of the mallard's feeding design maximized for specific proportions of performance that are contributed by pecking and filter feeding mechanisms.The earlier described anatomy and formal analyses of the three mechanisms in the mallard served as the initial conditions used in simulation models. Four (...) elements of the feeding system were chosen that play a major role in all three mechanisms. For each element, the main parameter was selected: storage capacity of the rostral mouth cavity, transport capacity of the rostral mouth tube, storage capacity of the caudal mouth cavity and transport capacity of the caudal mouth tube. The boundary conditions for the simulation were determined from internal organismic constraints. The total food uptake of the mallard was regarded as the function to be maximized. This object function is the summation of the food uptake by one second of pecking and one second of filter feeding. The drinking mechanism was shown not to interfere, since that mechanism operates sufficiently whenever the pumping mechanism works properly. (shrink)

For each integer $n\geq 2,{\Bbb MV}_{n}$ denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in ${\Bbb MV}_{n}$ are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in ${\Bbb MV}_{n}$ are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When $A\in {\Bbb MV}_{3}$, the mentioned characterization of maximal subalgebras of A can be (...) given in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro. (shrink)

In this article, we describe and attempt to solve a puzzle arising from the interpretation of modified numerals like less than five and between two and five. The puzzle is this: such modified numerals seem to mean different things depending on whether they combine with distributive or non-distributive predicates. When they combine with distributive predicates, they intuitively impose a kind of upper bound, whereas when they combine with non-distributive predicates, they do not. We propose and explore in detail four solutions (...) to this puzzle, each involving some notion of maximality, but differing in the type of maximality involved and in the source of maximality. While the full range of data we consider do not conclusively favor one theory over the other three, we do argue that overall the evidence goes against the view that modified numerals lexically encode a ‘standard’ maximality operator, and suggests the need for a pragmatic blocking mechanism that filters out readings of sentences that are generated by the grammar but intuitively unavailable. (shrink)

Let I0 be a a computable basis of the fully effective vector space V∞ over the computable field F. Let I be a quasimaximal subset of I0 that is the intersection of n maximal subsets of the same 1-degree up to *. We prove that the principal filter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}^{\ast}(V,\uparrow )}$$\end{document} of V = cl(I) is isomorphic to the lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}(n, \overline{F})}$$\end{document} (...) of subspaces of an n-dimensional space over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{F}}$$\end{document}, a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma _{3}^{0}}$$\end{document} extension of F. As a corollary of this and the main result of Dimitrov (Math Log 43:415–424, 2004) we prove that any finite product of the lattices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\mathcal{L}(n_{i}, \overline{F }_{i}))_{i=1}^{k}}$$\end{document} is isomorphic to a principal filter of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{ L}^{\ast}(V_{\infty})}$$\end{document}. We thus answer Question 5.3 “What are the principal filters of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}^{\ast}(V_{\infty})?}$$\end{document} ” posed by Downey and Remmel (Computable algebras and closure systems: coding properties, handbook of recursive mathematics, vol 2, pp 977–1039, Stud Log Found Math, vol 139, North-Holland, Amsterdam, 1998) for spaces that are closures of quasimaximal sets. (shrink)

IMTL logic was introduced in [12] as a generalization of the infinitely-valued logic of Lukasiewicz, and in [11] it was proved to be the logic of left-continuous t-norms with an involutive negation and their residua. The structure of such t-norms is still not known. Nevertheless, Jenei introduced in [20] a new way to obtain rotation-invariant semigroups and, in particular, IMTL-algebras and left-continuous t-norm with an involutive negation, by means of the disconnected rotation method. In order to give an algebraic interpretation (...) to this construction, we generalize the concepts of perfect, bipartite and local algebra used in the classification of MV-algebras to the wider variety of IMTL-algebras and we prove that perfect algebras are exactly those algebras obtained from a prelinear semihoop by Jenei's disconnected rotation. We also prove that the variety generated by all perfect IMTL-algebras is the variety of the IMTL-algebras that are bipartite by every maximal filter and we give equational axiomatizations for it. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π2 1 comprehension. An MF space is defined to be a topological space of the form MF(P) with the topology generated by $\lbrace N_p \mid p \in P \rbrace$ . Here P is a poset, MF(P) is the set of maximal filters on P, and $N_p = \lbrace F \in MF(P) \mid p \in F \rbrace$ . If the poset P is (...) countable, the space MF(P) is said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, "every countably based MF space which is regular is homeomorphic to a complete separable metric space," is equivalent to Π2 1-CA0. The equivalence is proved in the weaker system Π1 1-CA0. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π2 1 comprehension. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π12 comprehension. An MF space is defined to be a topological space of the form MF with the topology generated by {Np ∣ p ϵ P}. Here P is a poset, MF is the set of maximal filters on P, and Np = {F ϵ MF ∣ p ϵ F }. If the poset P is countable, the space MF is said (...) to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, “every countably based MF space which is regular is homeomorphic to a complete separable metric space,” is equivalent to. The equivalence is proved in the weaker system. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π12 comprehension. (shrink)

Inspired by locale theory, we propose “pointfree convex geometry”. We introduce the notion of convexity algebra as a pointfree convexity space. There are two notions of a point for convexity algebra: one is a chain-prime meet-complete filter and the other is a maximal meet-complete filter. In this paper we show the following: the former notion of a point induces a dual equivalence between the category of “spatial” convexity algebras and the category of “sober” convexity spaces as well (...) as a dual adjunction between the category of convexity algebras and the category of convexity spaces; the latter notion of point induces a dual equivalence between the category of “m-spatial” convexity algebras and the category of “m-sober” convexity spaces. We finally argue that the former notion of a point is more useful than the latter one from a category theoretic point of view and that the former notion of a point actually represents a polytope and the latter notion of a point properly represents a point. We also remark on the close relationships between pointfree convex geometry and domain theory. (shrink)

In this paper we give an axiom system of a logic which we call an approximation logic (AL), whose Lindenbaum-Tarski algebra is a strong Bunge algebra (or simply s-Bunge algebra), and show thatFor every s-Bunge algebra , a quotient algebra by a maximal filter is isomorphic to the simplest nontrivial s-Bunge algebra ;The Lindenbaum algebra of AL is an s-Bunge algebra;AL is complete;AL is decidable.

In this paper we shall first show that for every weak DeMorgan algebra $L$ of order $n$ , there is a quotient weak DeMorgan algebra $L{\sim}$ which is embeddable in the finite WDM-$n$ algebra $\Omega $. We then demonstrate that the finite WDM-$n$ algebra $\Omega $ is functionally free for the class $CL$ of WDM-$n$ algebras. That is, we show that any formulas $f$ and $g$ are identically equal in each algebra in $CL$ if and only if they are identically (...) equal in $\Omega $. Finally we establish that there is no weak DeMorgan algebra whose quotient algebra by a maximal filter has exactly seven elements. (shrink)

This paper gives a formalization of general topology in second-order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF denote the set of maximal filters on P endowed with the topology generated by {Np | p ∈ P}, where Np = {F ∈ MF | p ∈ F}. We define a countably based MF space to be a space of the form MF for (...) some countable poset P. The class of countably based MF spaces includes all complete separable metric spaces as well as many nonmetrizable spaces. The following reverse mathematics results are obtained. The proposition that every nonempty Gδ subset of a countably based MF space is homeomorphic to a countably based MF space is equivalent to [Formula: see text] over ACA0. The proposition that every uncountable closed subset of a countably based MF space contains a perfect set is equivalent over [Formula: see text] to the proposition that [Formula: see text] is countable for all A ⊆ ℕ. The proposition that every regular countably based MF space is homeomorphic to a complete separable metric space is equivalent to [Formula: see text] over [Formula: see text]. (shrink)

Sheaves of structures are useful to give constructions in universal algebra and model theory. We can describe their logical behavior in terms of Heyting‐valued structures. In this paper, we first provide a systematic treatment of sheaves of structures and Heyting‐valued structures from the viewpoint of categorical logic. We then prove a form of Łoś's theorem for Heyting‐valued structures. We also give a characterization of Heyting‐valued structures for which Łoś's theorem holds with respect to any maximal filter.

The main aim of the paper is to solve a problem posed in Di Nola et al. (Multiple Val. Logic 8:715–750, 2002) whether every pseudo BL-algebra with two negations is good, i.e. whether the two negations commute. This property is intimately connected with possessing a state, which in turn is essential in quantum logical applications. We approach the solution by describing the structure of pseudo BL-algebras and pseudo hoops as important families of quantum structures. We show when a pseudo hoop (...) can be embedded into the negative cone of the reals. We give an equational base characterizing representable pseudo hoops. We also describe some subvarieties: normal-valued, and varieties where each maximal filter is normal. We produce some noncommutative covers and extend the area where each algebra is good. Finally, we show that there are uncountably many subvarieties of pseudo BL-algebras having members that are not good. (shrink)

In the present paper, we introduce the notions of quasi-Boolean algebras as the generalization of Boolean algebras. First we discuss the related properties of quasi-Boolean algebras. Second we define filters of quasi-Boolean algebras and investigate some properties of filters in quasi-Boolean algebras. We also show that there is a one-to-one correspondence between the set of filters and the set of filter congruences on a quasi-Boolean algebra. Then we investigate the prime filters and maximal filters of quasi-Boolean algebras, showing (...) that the prime filters of a quasi-Boolean algebra are precisely the maximal filters and the prime spectrum of a quasi-Boolean algebra is a compact Hausdorff topological space. Finally, we define and study the reticulation of a quasi-Boolean algebra. (shrink)

An ordering (≤K) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size.

In sensory biology, a major outstanding question is how sensory receptor cells minimize noise while maximizing signal to set the detection threshold. This optimization could be problematic because the origin of both the signals and the limiting noise in most sensory systems is believed to lie in stimulus transduction. Signal processing in receptor cells can improve the signal‐to‐noise ratio. However, neural circuits can further optimize the detection threshold by pooling signals from sensory receptor cells and processing them using a combination (...) of linear and nonlinear filtering mechanisms. In the visual system, noise limiting light detection has been assumed to arise from stimulus transduction in rod photoreceptors. In this context, the evolutionary optimization of the signal‐to‐noise ratio in the retina has proven critical in allowing visual sensitivity to approach the limits set by the quantal nature of light. Here, we discuss how noise in the mammalian retina is mitigated to allow for highly sensitive night vision. (shrink)

We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a connection between (...) our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article provides a bridge between Colombeau theory of generalized functions and non-standard analysis. (shrink)

§1. Introduction. Ideals and filters of subsets of natural numbers have been studied by set theorists and topologists for a long time. There is a vast literature concerning various kinds of ultrafilters. There is also a substantial interest in nicely definable ideals—these by old results of Sierpiński are very far from being maximal— and the structure of such ideals will concern us in this announcement. In addition to being interesting in their own right, Borel and analytic ideals occur naturally (...) in the investigations of compact subsets of the space of all Baire class 1 functions on a Polish space, see [12, 18]. Also, certain objects associated with such ideals are of considerable interest and were quite extensively studied by several authors. Let us list here three examples; in all three of them I stands for an analytic or Borel ideal.1. The partial order induced by I on P: X ≥I Y iff X \ Y ϵ I and the partial order.2. Boolean algebras of the form P/I and their automorphisms.3. The equivalence relation associated with I: XEI Y iff X Δ ϵ I.In Section 4, we will have an opportunity to state some consequences of our results for equivalence relations as in 3. (shrink)

In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we show (...) that Grzegorczyk points are maximal contracting filters in the sense of De Vries, but the converse inclusion is not necessarily true. We also compare the notions of a Grzegorczyk point and an ultrafilter, and establish several properties of topological spaces based on Grzegorczyk structures. The main results of the paper are representation and completion theorems for G-structures. We prove both set-theoretical and topological representation theorems for various classes of G-structures. We also present topological object duality theorem for the class of complete G-structures and the class of concentric spaces, both restricted to structures which satisfy countable chain condition. We conclude the paper with proving equivalence of the original Grzegorczyk axiom with the one accepted by us as axiom. (shrink)

Consider any subvariety of BL-algebras generated by a single BL-chain which is the ordinal sum of the standard MV-algebra on [0, 1] and a basic hoop H. We present a geometrical characterization of elements in the finitely generated free algebra of each of these subvarieties. In this characterization there is a clear insight of the role of the regular and dense elements of the generating chain. As an application, we analyze maximal and prime filters in the free algebra.

continent. 2.2 (2012): 155–158 Michel Serres. Biogea . Trans. Randolph Burks. Minneapolis: Univocal Publishing. 2012. 200 pp. | ISBN 9781937561086 | $22.95 Conveying to potential readers the significance of a book puts me at risk of glad handing. It’s not in my interest to laud the undeserving, especially on the pages of this journal. This is not a sales pitch, but rather an affirmation of a necessary work on very troubled terms: human, earth, nature, and the problematic world we made. (...) It is this world that aspirates the silence (so to speak), and therefore the subject which, along with the development of the “made world” exports the excess augmentation of the cosmically missing, this silence of the natural, et cetera. Had we learned from Locke that lesson of “labor,” to consume what we need… but perhaps we need more than what matters? Serres’ Biogea has several functions on this manner, if it is indeed a book to be consumed. First, readers searching for novelistic entertainment have a place to dwell. Biogea deserves a place in your back pocket; biographical generosity and poetic fluidity should satisfy most textual fetishes. For lay philosophers who want to refresh their acumen, Biogea deserves a place on the book shelf, one already reads a sorely needed postmodern tune-up here. Serres’ style is clearly French; he leaves few cheese crumbs on his words, rather preciseness and breathing in the work give way to a sweeping manner that breaks the narrative line of sight. A circular narrative and anachronistic fragmentation of terms allows an abyssal atmosphere to swell, if only to pump into the book the externality of its broader text. Biogea aspires to a higher standard and the book, at times, is thinking this negentropic problem too. Univocal, the publisher, has crafted a book appropriate for the hands to hold and the translations are an achievement of an otherwise difficult writer to translate. Terms are the conditions of a broader text. It is important to note that Serres’ content is as much a thinking of terminal ports. There is a regard for the transportation technology of the written word. For me, this is the mark of genius, a craftiness that tells of a book device that I may trust. Serres is an accomplished thinker and a necessary voice to check the putative trendiness of anti-postmodernist and market-driven theory of endless cultural liquidation. Offering interventions on subjectivity as an open system we are given a chance to affirm the human, not merely to discard it, but to engage its poetic image emotion, the calibratory silent sense of the analogic world; the terms on which we base our efforts. 1 The human is the center of its own negation, constantly mediating it. Something deeper at stake appears in the work then, and it is quite obvious from the onset. Certainly, a book is an intensification of possible text and those who brought this actual book into existence have captured a rarity in regards to the subject matter and artistic accomplishment. I mentioned terms as conditions, so let us understand Biogea as bio-yea, a yes to bios . An affirmation of living and accepting presence for all of its defiance of images, words, and things temporal. Therefore Serres’ existence and its existants plays parts; out of linearity and still like a porous bone pumping blood it manufactures into the fleshy life it becomes. Starting from a man named silence chaos emerges, or the man “Old Taciturn” takes up a journey anticipating a great flood. In other words, a development akin to the one in Genesis. In dealing with this ancestral occupation, fusing Genesis with contemporary philosophical terms, Serres initiates this anachronistic fragmentation under the forming subjectivity of his own autobiography. This mutation in the open system is precisely one of Serres’ terms. There an abyss is at work, stated, but also measured by heels on the ground—the abyss dispatching earthen tensions, that which plays our tunes, that which we abide by and recognize in volcanoes, rivers, oceans, earthquakes and weaponry in the battles of the world. Set in later stages of the book, such tensions are harnessed through scientific principles in an attempt to unify the terms of natural force if only to terminate the world. Thus the elevation of the earth into the world is clearly set forth. Here already, and few pages in, a resonance is set forth under appellations such as the river Garonne, a subjectivity as much as it is inhuman, the river is the inhuman that makes us human. I get the sense that Serres is taking up a challenge issued by Wallace Stevens; namely, that the great poems of heaven and hell have been written, but that only the poem of the earth has resisted composition. 2 On this level we cannot avoid the killing factor of silence, given that our cognition blocks its pure, radical obliteration. Thus a silence of attunement to the earth is in a novel dialectic of the rithmic and rhythm. A technological world, a triumph of termination is set forth. If a text imposes its will given the reader who authorizes it, it is made to convey or convect a presupposition to a reader or its inhabitant(s). Text is therefore both, in-content, contenting, contentedness, and in reading it, a way to navigate self-destruction (dis-content). Here then would one note that the “inhuman” reveals itself, “an aperiodic rhythm of lovers and beloved…the sea as our friend…but as our enemy…maternal vivifying sea.” The sea is an open book, or vaginal birth canal, where the engagement of text comes forth: “…woman sea, open vulva.” One sees like the sea, but only after it, when the uninhabitable truth of inhabiting it switches the polarity of the sailors soul: “I was seeing like the sea” (9-11). In other words, we are invited to embrace the nonsense of the visible. At this point I am taken to Jean-François Lyotard’s work The Inhuman , specifically the first entry on negentropy that would be congruent with Serres’ thematic. 3 The human being exports, deports, or transplants its relation through text, through the system— and this is its sense or relation to silence, to music. Unaware of Serres’ proximity to this work, the concept of gender interrelation as regards a solar catastrophe runs clear. It would be, on this basis, that Serres references his peers, the other texts that, as mentioned above, are discarded in philosophy today. For students of philosophy what we have here is perhaps a gift, a needed project. If silence and death are at work, there is a political valence to deal with, and here, much like the domain of the text and the dominion of the reader, we confront the world of natural, fluid violence. The anti-postmodernist critique is in part based on a weak idea that the loss of ideology, of a world vision, motivates the “correlationist” project. 4 Serres seems to offer another way to view this when he notes that whereas persons “sometimes kill,” it is clearly “the collective” that “always kills” (17). What is the collective today, if not an organizing function we never see yet acts in its favor in the name of truth? One feels a sense of enigma here, if only to link to what Stevens remarked of communism as a “grubby faith,” providing this applies for capitalism as well, namely any ideology of progress overly interested in absolutes. Here we get the sense that the inhuman, silence, this type of killing, always killing, could not be matched by human-made, political dynamos. Or that if it comes to an equilibrium, a catastrophe is never too far from us to read with our heels. We are left to note that the forces of nature presuppose and permeate political systems, the more these systems obtain force, the more the system takes upon itself the proper name of nature that motivates its dissemination, albeit falsely. This note, that in an age of ecocide and technological captivity (sustainability and transparency) political regimes won’t grow our soul-learning ears any larger than our tongues, stands clear to us. The promise of technological desubjectification is here pushed aside. Regarding politics, Serres illustrates this fact: Where did this corpse come from? Who was it? Who killed it? I don’t know. I won’t try to find out. I refuse to get vengeance for it. And I only see Garonne. For our victims, today, are the rivers, too. Their waters have irrigated my life, enchanted my thought, invigorated my body; I’ve known them to be threatening, untamable, as dangerous as the sea when it rages. Yes, murderous. They decided to control their courses; dams, sometimes senseless, destroying sites and valleys, reduced entire populations to servile displacements; programs for the irrigation of thirsty farmland, often beneficial of course, completed their drying up.(22) Serres enters into his idea concerning the captivity of language from the natural into a world system: For thousands of years, we have been licking things with our tongues, covering and daubing them so as to appropriate things for ourselves. If language boils down to a convention, this convention took place between the speakers without consulting the thing named, become as a result the property of those who covered it in this way with their drawn or voiced productions. Malfeasance analyzes these acts of appropriation. Thus every inert object, every living thing as well, sleeps under the covers of signs, a little in the way that, today, a thousand posters shouting messages and ugly riots of color drown, with their filthy flood, the landscapes, or better, exclude them from perception because the meaning, almost nil, of this false language and these base images forms an irresistible source of attraction to our neurons and eyes. This appropriation covers the world’s beauty with ugliness. (38-39) Technological concealment coming to bear, we begin to get a sense of another commentary on the condition of sensing, driving home the necessity of a text dealing with such subject matter to be what its terms insist. Thus toward new openings: The new opening. As low beneath our feet as you like, the Biogea opens us to another space, high enough for us to be able to acquire a wisdom there, that of redeveloping this same place differently from our fathers, this place that’s still politically cut up by old hatreds, beneath the flood of tears and blood that we call history. Without this soft place, spiritually very old, but newly conceived in this way, without the juridical construction of a common good, opposed to our filthy ownership, I don’t see how our planet, hard, will survive. Hardness that depends on a softness, material belonging that depends on this temporary rented location (51). Serres enters into a summit on the content and the structure of his work. Archimedes is brought in with the concept of three volcanoes. Meaning fire, but as well earth, water, air. For it was Archimedes’ war machines that sought to lift the earth, thus bringing in the question of principles of science: “can a principle be invented while controlling its consequences?” (66-7). May the earth be put in a sentence, terminated by terminology, appellations, gone wild? By means of these element-dominating laws, this old physicist began to tear nature away from the ancient myths; by a strange return, today we’re plunging our successes back into the anxieties and terrors from which that ancient physics was born. Yes, our new history of science and technology is plunging, today, as though in a loop, into the fundamental human myths from which Empedocles’ first laws came. A major progression and a regression on the nether side of the origins. Consequently, the contemporary time requires that we try to return to that unity in which the principles of hate and love are at the same time human, living, inert and global. We will never attain a deontology of our knowledge and actions without thinking the subjective, the objective, the collective, and the cognitive all together simultaneously. Here, hate and love are the result of these four components.(71) Working then on the concept of fire-starting mirrors to the atomic annihilation of the Second War, Serres works into the subjectivity in question on the matter of rhythm—say rithmic— precisely at that point: Knowledge is changing today. The all-political is dying; the monarchy of the sciences said to be hard is coming to a close. The science of the things of the world will have to communicate just as much as the things of the world do, which do it much better than humans do, who don’t always want to do it. Let’s celebrate two changes this morning. The first one strikes a new blow to our narcissism. No, knowledge and the world don’t resemble our analytical enjoyments of refined cutting up, of endless debates and of exclusions full of hate. They, on the contrary, form a bloc and a sum, alliance and alloys. Uniting the fields of knowledge among themselves the way the things are connected among themselves, the second newness puts into place sets united by interlacing, webs and simplexes that combine with the things of the world, themselves combined, the combined knowledge that understands them.(130-1) Biogea closes on its opening flood thematic, approaching the initial telos of Genesis. Here the trees are brought into a position with atmosphere, the opaque abyssal reservoir, the tomb of the sun, sea in the polarity of the earthen heaven and hell. The poem of the earth then is silent but deadly, indeed, as funny as that phrase is, mainly a tomb gas. The meaning of the living and the non-meaning of things converge in the muteness of the world; this meaning and non-meaning plunge there and come out, the ultimate eddy. Mundus patet: through a fissure, through an opening, a fault, a cleft come noises, calls as small as these apertures. I’m listening, attentive, I’m translating, I’m advancing in the scaled-down meaning and science. Mundus patet: should the world open greatly, it will launch me into its silence. The totality remains silent. Knowledge expanded in elation. White origin of meaning, fountain of joy. (198) Final Remarks One test of a review is the long term trajectory the referee thinks the book will have. I see Serres’ text lending greatly into the vision of Biogea . In fact, in the vision of the novel inquiries of Stephen Jay Gould’s work there is something to be thought on the level of the individual and the species; namely, that humanity and its uniqueness is in its deferral, its thinking and naming, a thinking surrounded by silence that filters into everything, that pulls us through the world, the kinetic pulse we recognize, and all of that we cleave away in the base philosophical maxim of difference itself. Unique individuals are spatial creatures: we dwell, and we ought to get good at it. Yet this is an imaginative space that, if you are crazy enough to believe it, de-term-ine the conditions of its own terms. That is why we are not merely creating spaces on the acceleration of time, or so this ignoramus thinks, to accidentally transcend. Imagination already has this insatiable silence that we drink up and fail to manifest. Space is timeless. The imagination itself, shared by humans for themselves, their objects, and the species as a whole, is a non-defined space of relation; a whole human trajectory as part of nature, and part of worlds that are the other side of thinking nature, the consequence of it, at least our attempt to do so. Our survival is based on our deliberation, our caution, our natural deconstructive sense toward this silence that is already part of the song, sung, singing of this century without end. Good books will let us inhabit this space and recognize a form of life. Serres’ text moves toward dwelling, as noted, in masterful and accessible ways. The pitched battles are the falling replays of anemic and dead politics. As soon as we realize there is humanity, we may be able to enjoy the end of it, our inhuman capability of listening to silence. NOTES 1. See Michel Serres. The Parasite . Minneapolis: University of Minnesota Press. 2007. 2. Wallace Stevens, “Imagination as Value” [ca. 1945], in Collected Poetry and Prose . New York: The Library of America. 1997. 724-39. 3. Jean-François Lyotard. The Inhuman: Reflections on Time . Trans. Geoffrey Bennington & Rachel Bowlby. Stanford, CA: Stanford University Press. 1992. 4. See the introduction: Quentin Melliassoux. After Finitude: An Essay on the Necessity of Contingency . Trans. Ray Brassier. New York: Continuum. 2008. EDITOR'S NOTE: This review was updated on August 8, 2012. Substantial edits include block quotes from the book under review as well as the inclusion of comments from the author. (shrink)

Given a target area and a location-aware social network, the location-aware influence maximization problem aims to find a set of seed users such that the information spread from these users will reach the most users within the target area. We show that the problem is NP-hard and present an approximate algorithm framework, namely, TarIM-SF, which leverages on a popular sampling method as well as spatial filtering model working on arbitrary polygons. Besides, for the large-scale network we also present a coarsening (...) strategy to further improve the efficiency. We theoretically show that our approximate algorithm can provide a guarantee on the seed quality. Experimental study over three real-world social networks verified the seed quality of our framework, and the coarsening-based algorithm can provide superior efficiency. (shrink)

In this paper, the notions of tense operators and tense filters in \-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \-algebras, tense \-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \-algebra is complete sublattice of \\) of all filters of \-algebra \. Also, maximal tense filters and simple tense \-algebras and the relation between them are studied. Finally, the notions of (...) tense congruence relations in tense \-algebras and strict tense \-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided. (shrink)

In this paper, the notions of tense operators and tense filters in \-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \-algebras, tense \-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \-algebra is complete sublattice of \\) of all filters of \-algebra \. Also, maximal tense filters and simple tense \-algebras and the relation between them are studied. Finally, the notions of (...) tense congruence relations in tense \-algebras and strict tense \-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided. (shrink)

No evangelistic erroneous network of ideas can guarantee the satisfaction of these two demands : (1) propagate the network without revision and (2) completely insulate itself against losses in credibility and adherents through criticism. If a network of ideas is false, or inconsistent or fails to solve its intended problem, or unfeasible, or is too costly in terms of necessarily forsaken goals, its acceptability may be undermined given only true assumptions and valid arguments. People prefer to adopt ideologies that (i) (...) are logically consistent, (ii) are more truth-like and of higher information content than their rivals, (iii) are systematically organised, (iv) solve their problems better than their rivals, (v) do not contain unfeasible demands, and (vi) do not contain uneconomic demands. Truth and validity therefore act as Darwinian-like filters on ideologies. Using Popper's notion of situational analysis and with reference to Darwinian evolution, considered as a special case of the former, and Bartley's theory of comprehensively critical rationalism I argue that a propagandist cannot guarantee his message or his movement from sound criticism. All positions are in a methodological sense open to argument. Moreover, the logic of a propagandist's situation constrains him into making his message and himself open to criticism in order to maximize its chances of being propagated through the population. But he then loses control of the message in two respects. Firstly, his audience are disposed to select from the competing ideas they encounter those that satisfy (i) to (vi) because of man's evolutionary history. Secondly, he cannot guarantee protection from criticism even a privileged section of his message because he cannot predict in a systematic way what logical repercussions each protective reformulation of the ideology will have on other sections of the ideology and what criticism the ideology will encounter. He cannot do the latter because of certain logical properties of theories that endow them with unfathomable depths. Marxism and Freudianism serve as case studies, especially for the analysis of Popper's notion of the immunizing stratagem, a methodological/logical device that is supposed to save theories from criticism. "Immunizing stratagems" either abandon the ideology they are meant to protect or seriously lower its chances of being reproduced. (shrink)

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for iterated contours of sequential cascades. A related problem of continuous extension of maps between maximal elements of sequential cascades to full subcascades is solved in full generality.

Nowadays, depression is the world’s major health concern and economic burden worldwide. However, due to the limitations of current methods for depression diagnosis, a pervasive and objective approach is essential. In the present study, a psychophysiological database, containing 213 subjects, was constructed. The electroencephalogram signals of all participants under resting state and sound stimulation were collected using a pervasive prefrontal-lobe three-electrode EEG system at Fp1, Fp2, and Fpz electrode sites. After denoising using the Finite Impulse Response filter combining the (...) Kalman derivation formula, Discrete Wavelet Transformation, and an Adaptive Predictor Filter, a total of 270 linear and nonlinear features were extracted. Then, the minimal-redundancy-maximal-relevance feature selection technique reduced the dimensionality of the feature space. Four classification methods distinguished the depressed participants from normal controls. The classifiers’ performances were evaluated using 10-fold cross-validation. The results showed thatK-Nearest Neighbor had the highest accuracy of 79.27%. The result also suggested that the absolute power of the theta wave might be a valid characteristic for discriminating depression. This study proves the feasibility of a pervasive three-electrode EEG acquisition system for depression diagnosis. (shrink)

Get the results your camera was meant to deliver With the D700, you've stepped up to a high-performance camera. The possibilities offered by its 12.1-megapixel, FX-format CMOS sensor are exhilarating. This guide helps you take full advantage of every feature you paid for, offering clear and comprehensive directions for setting up the camera, choosing modes, selecting lenses, and much more. With detailed guidance for working with lighting, exposure, and depth of field plus advanced shooting techniques for many different situations, it's (...) your camera's perfect partner. Customize the D700's settings and learn how to use them all Maximize Live View and use single-point and dynamic-area autofocus Explore original, optional, and custom picture controls Investigate wide-angle lenses, VR and DX lenses, filters, and lens accessories Learn secrets for getting great shots of sporting events, concerts, wildlife, products, and people. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:25 MORALITY AS A BACK-UP SYSTEM: HUME'S VIEW? The sense of duty is a useful device for helping men to do what a really good man would do without a sense of duty..... Nowell-Smith A certain picture of morality — arguably a Humean one — has come to have a prominent place in contemporary philosophy. On this picture, morality, as Richard Brandt asserts, is "a back-up system, which operates (...) when spontaneous personal caring fails 2 to motivate us to do as we ought." Morality — at least in the form of moral principles, whose force is felt through one's sense of duty — is, on this view, ideally superfluous. As a guide for one's own conduct it is needed only insofar as the agent's affective network is deficient. If one only spontaneously desired a, cared about b, cared for c, felt aversion towards d as, ideally, one should, moral principles and a sense of duty would be of no use. There are good reasons for supposing that this is Hume's view. After all, his characterization of acting from duty is more than a little disparaging: When any virtuous motive or principle is common in human nature, a person, who feels his heart devoid of that motive, may hate himself upon that account, and may perform the action without the motive, from a certain sense of duty, in order to acquire by practice, that virtuous principle, or at least, to disguise to himself,,as much as possible, his want of it. I will argue, however, that there is tension in Hume's ethics between two lines of thought. According to the first line of thought, and the one 26 usually associated with Hume, good conduct is conduct which is spontaneously prompted by virtuous desires. Unless our desires either are not what they should be or are motivationally weak, there is no need for mediation or tempering by a sense of duty or moral principles. According to the second line, the very good desires of a very good person may nonetheless need to be filtered, tempered, redirected or checked. This line is most evident in "Of the Origin of the Natural Virtues and Vices." Before arguing that these strains of thought are in tension in Hume's ethics, I need to clarify what is at issue and to develop the two competing pictures of moral motivation. First the issue. The issue is not 'Who is better: someone with a sense of duty but corrupt desires or someone with no sense of duty but ideal desires?' Nor is the issue one of the moral worth of actions ('Can an action have moral worth if it is not performed out of duty?') The issue, rather, is how to characterize morally good (or right) conduct. What role, if any, does a sense of duty or a Butlerian principle of reflection, i.e., an overarching, guiding conception of what is right or good which is 'juridically' supreme within the self, play in good conduct? Is morally good conduct ideally a matter of acting as one should from the proper desires? Or should the desires be governed and guided by moral principles? Consider two models of moral conduct. Model I: Morality as a Back-Up System On this picture, wrongness in conduct is traceable to an affective deficiency. The claim underlying this picture seems to be as follows: One 27 acts wrongly because one's passions are not quite what they should be. One person cheats in her business dealings because she cares too little about the welfare of others (and too much about her own); another is harsh and abrupt to a student because he cares too little about his students' concerns and is jealous and possessive when it comes to 'his time.' In each case the problem can be traced to an affective deficiency. Hume appears to be supporting this view when he asserts, "it may be establish'd as an undoubted maxim, that no act can be virtuous, or morally good, unless there be in human nature some motive to produce it, distinct from a sense of its morality' (T 479). A few pages later he writes, "[E]very immorality... (shrink)

Information is a peculiar quantity. Unlike matter and energy, which are conserved by the laws of physics, the aggregation of knowledge from many sources can in fact produce more information (synergy) or less (redundancy) than the sum of its parts. This feature can endow groups with problem‐solving strategies that are superior to those possible among noninteracting individuals and, in turn, may provide a selection drive toward collective cooperation and coordination. Here we explore the formal properties of information aggregation as a (...) general principle for explaining features of social organization. We quantify information in terms of the general formalism of information theory, which also prescribes the rules of how different pieces of evidence inform the solution of a given problem. We then show how several canonical examples of collective cognition and coordination can be understood through principles of minimization of uncertainty (maximization of predictability) under information pooling over many individuals. We discuss in some detail how collective coordination in swarms, markets, natural language processing, and collaborative filtering may be guided by the optimal aggregation of information in social collectives. We also identify circumstances when these processes fail, leading, for example, to inefficient markets. The contrast to approaches to understand coordination and collaboration via decision and game theory is also briefly discussed. (shrink)

A methodology is proposed as a tool for explanation of form in zoomorphology, in particular its design, diversity, and transformation. An alternate use of descriptive, inductive/comparative, and deductive methods is suggested. The basic concepts required are summarized. Following an extensive anatomical analysis a specific deductive methodology is developed, comprising three major parts: 1) Formal analysis of systems, using optimal design. 2) Transformation of an initial system's model by simulating modifications via maximizing the model for specific functional requirements. 3) Testing by (...) comparison of deduced modifications with real systems having the maximized functional capacity, trends in specific morphoclines, and empirical analogues from technology.The methodology produces a morpho-space of modifications that has the form of branching pathways. That pattern results from innovation, bifurcation, and radiation moments in the deduction. The morpho-space is converted in a mechano-space by including next to constructional characters those of operation and rolefulfilment. If the initial system is verified as the ancestor and the transformation-function is verified as the evolutionary theme of change, the explanation turns -in addition to a function anatomical one- also into an evolutionary one. The method is illustrated by reviewing some recent analyses about avian feeding: maximization of avian pecking for probing and filter feeding capacities. (shrink)

We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$. In addition, we show that Shelah’s poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$.

In this work we will study Tarski algebras endowed with a subordination, called subordination Tarski algebras. We will define the notion of round filters, and we will study the class of irreducible round filters and the maximal round filters, called ends. We will prove that the poset of all round filters is a lattice isomorphic to the lattice of the congruences that are compatible with the subordination. We will prove that every end is an irreducible round filter, and (...) that in a topological subordination Tarski algebra A, every irreducible round filter is an end iff A is a monadic subordination Tarski algebra. As corollary of this result we have that the variety of monadic Tarski algebra can be characterised as the topological Tarski algebras where every irreducible open filter is a maximal open filter. (shrink)

This thesis divides naturally into two parts, each concerned with the extent to which the theory of $L$ can be changed by forcing.The first part focuses primarily on applying generic-absoluteness principles to how that definable sets of reals enjoy regularity properties. The work in Part I is joint with Itay Neeman and is adapted from our paper Happy and mad families in $L$, JSL, 2018. The project was motivated by questions about mad families, maximal families of infinite subsets of (...) $\omega $ of which any two have only finitely many members in common. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the Solovay model, giving a new proof of Törnquist’s theorem that there are no infinite mad families in the Solovay model.In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of $L$ cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in fact there is an elementary embedding from the $L$ of the ground model to that of the proper forcing extension. With a view toward analyzing mad families under $\mathsf {AD}^+$ and in $L$ under large-cardinal hypotheses, in Chapter 4 we establish triangular versions of the Embedding Theorem. These are enough for us to use Mathias’s methods to show that there are no infinite mad families in $L$ under large cardinals and that $\mathsf {AD}^+$ implies that there are no infinite mad families. These are again corollaries of theorems about strong Ramsey properties under large-cardinal assumptions and $\mathsf {AD}^+$, respectively. Our first theorem improves the large-cardinal assumption under which Todorcevic established the nonexistence of infinite mad families in $L$. Part I concludes with Chapter 5, a short list of open questions.In the second part of the thesis, we undertake a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin cardinals. He defined remarkable cardinals, which can exist even in L, and showed that the Embedding Theorem is equiconsistent with the existence of a remarkable cardinal. His theorem resembles a theorem of Harrington–Shelah and Kunen from the 1980s: the absoluteness of the theory of $L$ to ccc forcing extensions is equiconsistent with a weakly compact cardinal. Joint with Itay Neeman, we improve Schindler’s theorem by showing that absoluteness for $\sigma $ -closed $\ast $ ccc posets—instead of the larger class of proper posets—implies the remarkability of $\aleph _1^V$ in L. This requires a fundamental change in the proof, since Schindler’s lower-bound argument uses Jensen’s reshaping forcing, which, though proper, need not be $\sigma $ -closed $\ast $ ccc in that context. Our proof bears more resemblance to that of Harrington–Shelah than to Schindler’s.The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend the Harrington–Shelah method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4, which asserts that if there are $X\subseteq \omega _1$ and a tree $T\subseteq \omega _1$ of height $\omega _1$ such that X is codable along T, then $L$ -absoluteness for ccc posets must fail.We complete the argument in Chapter 8, where we show that if in any $\sigma $ -closed extension of V there is no $X\subseteq \omega _1$ codable along a tree T, then $\aleph _1^V$ must be remarkable in L.In Chapter 9 we review Schindler’s proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound: a strongly $\lambda ^+$ -remarkable cardinal is enough to get $L$ -absoluteness for $\lambda $ -linked proper posets.Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. Adapting the methods of Neeman, Hierarchies of forcing axioms II, we are able to show that $L$ -absoluteness for $\left |\mathbf {R}\right |\cdot \left |\lambda \right |$ -linked posets implies that the interval $[\aleph _1^V,\lambda ]$ is $\Sigma ^2_1$ -remarkable in L.prepared by Zach Norwood.E-mail: [email protected]. (shrink)

The main topics of this thesis are cardinal invariants, P -points and MAD families. Cardinal invariants of the continuum are cardinal numbers that are bigger than $\aleph _{0}$ and smaller or equal than $\mathfrak {c}.$ Of course, they are only interesting when they have some combinatorial or topological definition. An almost disjoint family is a family of infinite subsets of $\omega $ such that the intersection of any two of its elements is finite. A MAD family is a maximal (...) almost disjoint family. An ultrafilter $\mathcal {U}$ on $\omega $ is called a P-point if every countable $\mathcal {B\subseteq U}$ there is $X\in $ $\mathcal {U}$ such that $X\setminus B$ is finite for every $B\in \mathcal {B}.$ This kind of ultrafilters has been extensively studied, however there is still a large number of open questions about them.In the preliminaries we recall the principal properties of filters, ultrafilters, ideals, MAD families and cardinal invariants of the continuum. We present the construction of Shelah, Mildenberger, Raghavan, and Steprāns of a completely separable MAD family under $\mathfrak {s\leq a}.$ None of the results in this chapter are due to the author.The second chapter is dedicated to a principle of Sierpiński. The principle $\left $ of Sierpiński is the following statement: There is a family of functions $\left \{ \varphi _{n}:\omega _{1}\longrightarrow \omega _{1}\mid n\in \omega \right \} $ such that for every $I\in \left [ \omega _{1}\right ] ^{\omega _{1}}$ there is $n\in \omega $ for which $\varphi _{n}\left [ I\right ] =\omega _{1}.$ This principle was recently studied by Arnie Miller. He showed that this principle is equivalent to the following statement: There is a set $X=\left \{ f_{\alpha }\mid \alpha \alpha $ then $f_{\beta }\cap g$ is infinite. Miller showed that the principle of Sierpiński implies that non $\left =\omega _{1}.$ He asked if the converse was true, i.e., does non $\left =\omega _{1}$ imply the principle $\left $ of Sierpiński? We answer his question affirmatively. In other words, we show that non $\left =\omega _{1}$ is enough to construct an $\mathcal {IE}$ -Luzin set. It is not hard to see that the $\mathcal {IE}$ -Luzin set we constructed is meager. This is no coincidence, because with the aid of an inaccessible cardinal, we construct a model where non $\left =\omega _{1}$ and every $\mathcal {IE}$ -Luzin set is meager.The third chapter is dedicated to a conjecture of Hrušák. Michael Hrušák conjectured the following: Every Borel cardinal invariant is either at most non $\left $ or at least cov $\left $. Although the veracity of this conjecture is still an open problem, we were able to obtain some partial results: The conjecture is false for “Borel invariants of $\omega _{1}^{\omega }$ ” nevertheless, it is true for a large class of definable invariants. This is part of a joint work with Michael Hrušák and Jindřich Zapletal.In the fourth chapter we present a survey on destructibility of ideals and MAD families. We prove several classic theorems, but we also prove some new results. For example, we show that every almost disjoint family of size less than $\mathfrak {c}$ can be extended to a Cohen indestructible MAD family is equivalent to $\mathfrak {b=c}$. A MAD family $\mathcal {A}$ is Shelah–Steprāns if for every $X\subseteq \left [ \omega \right ] ^{<\omega }\setminus \left \{ \emptyset \right \} $ either there is $A\in \mathcal {I}\left $ such that $s\cap A\neq \emptyset $ for every $s\in X$ or there is $B\in \mathcal {I}\left $ that contains infinitely many elements of X $ denotes the ideal generated by $\mathcal {A}$ ). This concept was introduced by Raghavan which is connected to the notion of “strongly separable” introduced by Shelah and Steprāns. We prove that Shelah–Steprāns MAD families have very strong indestructibility properties: Shelah–Steprāns MAD families are indestructible for “many” definable forcings that does not add dominating reals. According to the author’s best knowledge, this is the strongest notion that has been considered in the literature so far. In spite of their strong indestructibility, Shelah–Steprāns MAD families can be destroyed by a ccc forcing that does not add unsplit or dominating reals. We also consider some strong combinatorial properties of MAD families and show the relationships between them.The fifth chapter is one of the most important chapters in the thesis. A MAD family $\mathcal {A}$ is called $+$ -Ramsey if every tree that branches into $\mathcal {I}\left $ -positive sets has an $\mathcal {I}\left $ -positive branch. Michael Hrušák’s first published question is the following: Is there a $+$ -Ramsey MAD family? It was previously known that such families can consistently exist. However, there was no construction of such families using only the axioms of ZFC. We solve this problem by constructing such a family without any extra assumptions.In the fourth and fifth chapters, we introduce several notions of MAD families, in the sixth chapter we prove several implications and non implications between them. We construct several MAD families with different properties.In the seventh chapter we build models without P -points. We show that there are no P -points after adding Silver reals either iteratively or by the side by side product. These results have some important consequences: The first one is that is its possible to get rid of P -points using only definable forcings. This answers a question of Michael Hrušák. We can also use our results to build models with no P -points and with arbitrarily large continuum, which was also an open question. These results were obtained with David Chodounský.prepared by Osvaldo Guzmán GonzálezE-mail : [email protected] : https://arxiv.org/abs/1810.09680. (shrink)

One of the major arguments against Act consequentialism is that it has counterintuitive implications in many kinds of cases. One of the methods of avoiding these counterintuitive verdicts is through the use of a “Generalization Argument” such as that proposed by Marcus Singer in his (1961) book Generalization in Ethics, which is intended to be an improved version of the traditional “What if everyone did that?” approach to moral theory. This Generalization Argument, however, also has counterintuitive implications due to over-generalizing. (...) In the spirit of his nomenclature, I thus propose that a form of consequentialism that partially generalizes, in a sense explained below, can avoid some of these counterintuitive results. The purpose of my proposing this new theory is to explore the idea of using some filter to sort actions into the categories of permissible vs. impermissible, and then use a consequentialist maximizing framework to choose between only the permissible options. (shrink)

Epicurus holds, in _Key Doctrine_ 31, that what is just according to nature is a _súmbolon_ or sign of the interest there is in neither harming one another nor being harmed. Certain readings of this maxim equivocate this legal sign with other signs found in nature, thereby failing to give sufficient weight to the role of reciprocity in its production. Other readings simply import a legal sense from outside of Epicurean doctrine, thereby failing to explain what makes Epicurean _súmbola_ legal. (...) A final set of readings attempt to find a legal rule as a kind of innate concept or Kantian ‘scheme’. This article identifies new sources for understanding _súmbolon_, drawn principally but not exclusively from Aristotle’s _Eudemian Ethics_. This article offers an original argument that Epicurus adopts Aristotle’s’ image of the tally stick (_symbolon_) as a meeting of often divergent interests which constitutes something new and particularly valuable to the Epicurean: friendship. A theoretical argument is also advanced to support this reading which claims that one person’s reflection on a ‘divine image’ of the end (_telos_) is insufficient to constitute a _súmbolon_; rather real (as opposed to abstract or ideal) individual interests are filtered via the mechanism of the tally, that is via the meeting of two given individuals who together generate a sign (_symbolon_) of reciprocal interest in neither harming nor being harmed. (shrink)

The main purpose of this dissertation is to apply and develop new forcing techniques to obtain models where several cardinal characteristics are pairwise different as well as force many (even more, continuum many) different values of cardinal characteristics that are parametrized by reals. In particular, we look at cardinal characteristics associated with strong measure zero, Yorioka ideals, and localization and anti-localization cardinals.In this thesis we introduce the property “F-linked” of subsets of posets for a given free filter F on (...) the natural numbers, and define the properties “ $\mu $ -F-linked” and “ $\theta $ -F-Knaster” for posets in a natural way. We show that $\theta $ -F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. These kinds of posets led to the development of a general technique to construct $\theta $ - $\textrm {Fr}$ -Knaster posets (where $\textrm {Fr}$ is the Frechet ideal) via matrix iterations of ${<}\theta $ -ultrafilter-linked posets (restricted to some level of the matrix). The latter technique allows proving consistency results about Cichoń’s diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal characteristics associated with it are pairwise different. Another important application is to show that three strongly compact cardinals are enough to force that Cichoń’s diagram can be separated into 10 different values. Later on, it was shown by Goldstern, Kellner, Mejía, and Shelah that no large cardinals are needed for Cichoń’s maximum (J. Eur. Math. Soc. 24 (2022), no. 11, p. 3951–3967).On the other hand, we deal with certain types of tree forcings including Sacks forcing, and show that these increase the covering of the strong measure zero ideal $\mathcal {SN}$. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal characteristics of the continuum. Even more, Sacks forcing can be used to force that $\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$, which is the first consistency result where more than two cardinal characteristics associated with $\mathcal {SN}$ are pairwise different. To obtain another result in this direction, we provide bounds for $\operatorname {\mathrm{cof}}(\mathcal {SN})$, which generalizes Yorioka’s characterization of $\mathcal {SN}$ (J. Symbolic Logic 67.4 (2002), p. 1373–1384). As a consequence, we get the consistency of $\operatorname {\mathrm{add}}(\mathcal {SN})=\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$ with ZFC (via a matrix iteration forcing construction).We conclude this thesis by combining creature forcing approaches by Kellner and Shelah (Arch. Math. Logic 51.1–2 (2012), p. 49–70) and by Fischer, Goldstern, Kellner, and Shelah (Arch. Math. Logic 56.7–8 (2017), p. 1045–1103) to show that, under CH, there is a proper $\omega ^\omega $ -bounding poset with $\aleph _2$ -cc that forces continuum many pairwise different cardinal characteristics, parametrized by reals, for each one of the following six types: uniformity and covering numbers of Yorioka ideals as well as both kinds of localization and anti-localization cardinals, respectively. This answers several open questions from Klausner and Mejía (Arch. Math. Logic 61 (2022), pp. 653–683).Abstract prepared by Miguel Antonio Cardona-MontoyaE-mail: [email protected]: https://repositum.tuwien.at/handle/20.500.12708/19629. (shrink)