Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two transfer results, one on the VC-density and the other one, on the combinatorial property NTP2.

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical completeness theorem with respect to PA is obtained for LR.

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is obtained for LR.

A P-point ultrafilter over \(\omega \) is called an interval P-point if for every function from \(\omega \) to \(\omega \) there exists a set _A_ in this ultrafilter such that the restriction of the function to _A_ is either a constant function or an interval-to-one function. In this paper we prove the following results. (1) Interval P-points are not isomorphism invariant under \(\textsf{CH}\) or \(\textsf{MA}\). (2) We identify a cardinal invariant \(\textbf{non}^{**}({\mathcal {I}}_{\tiny {\hbox {int}}})\) such that every (...) filter base of size less than continuum can be extended to an interval P-point if and only if \(\textbf{non}^{**}({\mathcal {I}}_{\tiny {\hbox {int}}})={\mathfrak {c}}\). (3) We prove the generic existence of slow/rapid non-interval P-points and slow/rapid interval P-points which are neither quasi-selective nor weakly Ramsey under the assumption \({\mathfrak {d}}={\mathfrak {c}}\) or \(\textbf{cov}({\mathcal {B}})={\mathfrak {c}}\). (shrink)

Are sagging pants cool? Are cows food? Are women more submissive than men? Are blacks more criminal than whites? Taking the social world at face value, many people would be tempted to answer these questions in the affirmative. And if challenged, they can point to facts that support their answers. But there is something wrong about the affirmative answers. In this chapter, I draw on recent ideas in the philosophy of language and metaphysics to show how the assertion of (...) a generic claim of the sort in question ordinarily permits one to infer that the fact in question obtains by virtue of something specifically about the subject so described, i.e., about women, or blacks, or sagging pants. In the examples I’ve offered, however, this implication inference is unwarranted. The facts in question obtain by virtue of broad system of social relations within which the subjects are situated, and are not grounded in intrinsic or dispositional features of the subjects themselves. The background relations are obscured, however, and as a result, the assertion is at least systematically misleading; a denial functions to block the problematic implication. Revealing such implications or presuppositions and blocking them is a crucial part of ideology critique. (shrink)

Generics exhibit genericity, and though a theory of generics is closely connected to a theory of genericity, the two are distinct. They raise a host of interesting linguistic and philosophical issues, both separately and in their interaction. This chapter begins with a fairly manifest phenomenon one can observe in natural language. There is a range of sentences that, speaking intuitively, one can use to talk about kinds. It argues that there's no simple statistical criterion that systematically captures the patterns of (...) the truth and falsity of generics. Generics seem to not just be substantially independent of statistical facts in the world and at the time with respect to which they are evaluated. The chapter points‐out a likely form of context dependence in generics, and argues that on a quantificational approach to generics, the restrictor of the generic quantifier must be determined at least in part by the predicate at issue. (shrink)

This paper reports an experiment that investigates interpretive distinctions between two different expressions of generalization in Spanish. In particular, our aim was to find out when the distinction between generic statements (GS) such as Tigers have stripes and universally quantified statements (UQS) such as All tigers have stripes was acquired in Spanish-speaking children of two different age groups (4/5-year-olds and 8/9-year-olds), and then compare these results with those of adults. The starting point of this research was the semantic (...) distinction between GS and UQS in that the former admit exceptions, unlike the latter. On the other hand, several authors have observed a Generic overgeneralization effect (GOG) consisting in allowing for UQS to be felicitous in the face of exceptions, thus proposing that this “error” stems from GS being defaults (simpler, more easily learned and processed). In the current paper we aimed to test the “Generics as Default” (GaD) hypothesis by comparing GS and UQS in three different age ranges. Our data show that, overall, the accuracy of GS is greater than the accuracy of UQS. Moreover, we also confirm a hypothesized interaction between age and NP type (GS vs UQS). Further, we present several data points that are not predicted by the GaD, including an observed decline in the accuracy of GS in the older group of children as well as in adults, and that children fail at rejecting statements that are not considered to be true generalizations. (shrink)

This article1 investigates a particular use of generic sentences (or “characterizing” sentences, in the terminology of Krifka e.a. 1995), which is most prevalent with indefinite singular subjects. Such subjects cannot always be interchanged with bare plural NPs, as has been famously pointed out by Lawler (1973).

From off-brand products to elevator music, the "generic" is discarded as the copy, the knock-off, and the old. In The Copy Generic, anthropologist Scott MacLochlainn insists that more than the waste from the culture machine, the generic is a universal social tool, allowing us to move through the world with necessary frames of reference. It is the baseline and background, a category that includes and orders different types of specificity yet remains non-specific in itself. Across arenas as (...) diverse as city planning, social media, ethnonationalism, and religion, the generic points to spaces in which knowledge is both over-produced and desperately lacking. Moving through ethnographic and historical settings in the Philippines, Europe, and the United States, MacLochlainn reveals ways the "generic" is crucial to how things repeat, circulate, and are classified in the world. (shrink)

I have argued not that economics has no predictive content, but that it is limited, or at least has so far been limited to generic predictions. Now this is an important kind of prediction, and almost certainly a necessary preliminary to specific or quantitative predictions. But if the sketch of an important episode in the twentieth century history of the subject I have given is both correct and representative, then economics seems pretty well stuck at the level of (...) class='Hi'>generic prediction. And at least some influential economists and philosophers of economics seem well satisfied with stopping at the point of generic prediction. Or at least they give no other reason than its power to produce such predictions as a justification for the character of economic theory. But this leads to the question that is the title of my paper, is generic prediction enough? (shrink)

We point out a connection between reflection principles and generic large cardinals. One principle of pure reflection is introduced that is as strong as generic supercompactness of ω2 by Σ-closed forcing. This new concept implies CH and extends the reflection principles for stationary sets in a canonical way.

LetMbe a countably infinite ω-categorical structure. Consider Aut(M) as a complete metric space by definingd(g, h) = Ω{2−n:g(xn) ≠h(xn) org−1(xn) ≠h−1(xn)} where {xn:n∈ ω} is an enumeration ofMAn automorphism α ∈ Aut(M) is generic if its conjugacy class is comeagre. J. Truss has shown in [11] that if the set P of all finite partial isomorphisms contains a co-final subset P1closed under conjugacy and having the amalgamation property and the joint embedding property then there is a generic automorphism. (...) In the present paper we give a weaker condition of this kind which is equivalent to the existence of generic automorphisms. Really we give more: a characterization of the existence of generic expansions (defined in an appropriate way) of an ω-categorical structure. We also show that Truss' condition guarantees the existence of a countable structure consisting of automorphisms ofMwhich can be considered as an atomic model of some theory naturally associated toM. We do it in a general context of weak models for second-order quantifiers.The author thanks Ludomir Newelski for pointing out a mistake in the first version of Theorem 1.2 and for interesting discussions. Also, the author is grateful to the referee for very helpful remarks. (shrink)

It is a familiar point that we can use generic sentences to express generalisations that are tolerant to exceptions and then go on to state those exceptions explicitly. It is a less familiar point that switching the order of the generics has deleterious effects on their felicity. For example, the sequences ‘Ravens are black, but albino ravens aren’t’ is perfectly felicitous and judged to be true, whereas its reverse ‘Albino ravens aren’t black, but ravens are’ is infelicitous (...) and contradictory-sounding. This paper argues that such sequences pose a problem for extant theories of generics: while they have no trouble predicting the felicity of the first sequence of generics, they are unable to explain why reversing the order results in infelicity. I propose to account for these observations by adopting a dynamic semantic theory of generic sentences. (shrink)

It is natural to wish to study miniaturisations of Cohen forcing suitable to sets of low arithmetic complexity. We consider extensions of the work of Schaeffer [9] and Jockusch and Posner [6] by looking at genericity notions within the Δ2 sets. Different equivalent characterisations of 1-genericity suggest different ways in which the definition might be generalised. There are two natural ways of casting the notion of 1-genericity: in terms of sets of strings and in terms of density functions, as we (...) will see here. While these definitions coincide at the first level of the difference hierarchy, they turn out to differ at other levels. Furthermore, these differences remain when the remainder of the Δ02 sets are considered. While the string characterization of 1-genericity collapses at the second level of the difference hierarchy to 2-genericity, the density function definition gives a very interesting hierarchy at level w and above. Both of these results point towards the deep similarities exhibited by the n-c.e. degrees for n ≥ 2. (shrink)

A generic computation of a subsetAof ℕ is a computation which correctly computes most of the bits ofA, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory, where it has been noticed that frequently, it is more important to know how difficult a type of problem is in the general case than how difficult it is in the worst case. When we study this concept from a recursion theoretic (...) class='Hi'>point of view, to create a transitive relationship, we are forced to consider oracles that sometimes fail to give answers when asked questions. Unfortunately, this makes working in the generic degrees quite difficult. Indeed, we show that generic reduction is$\Pi _1^1$―complete. To help avoid this difficulty, we work with the generic degrees of density-1 reals. We demonstrate how an understanding of these degrees leads to a greater understanding of the overall structure of the generic degrees, and we also use these density-1 sets to provide a new a characterization of the hyperartithmetical Turing degrees. (shrink)

The article discusses the issue of how to categorize video games—not the medium of video games, but individual video games. As a lead in to this discussion, the article discusses video game specificity and genericity and moves on to genre theory. On the basis of this discussion, a cognitive experientialist genre framework is sketched, which incorporates both general points from genre theory and theories more specific to the video game domain. The framework is illustrated through a brief example. One virtue (...) of the framework is that it offers a way to bridge the gap between game ontology and player experience; a brief conclusion discusses how the breadth of this gap may depend upon player biographies and also outlines how further work may proceed. (shrink)

Open peer commentary on the article “Ethics: A Radical-constructivist Approach” by Andreas Quale. Upshot: I agree with some of Quale’s general conclusions, in particular that each individual knower is responsible for choosing among alternatives and the pragmatic consequences that are related to this choice. However, in adopting implicitly the premise according which individual human existence precedes coexistence or social existence, and in focusing on the cognitive operations of a “generic subject” (that is, a disembodied subject coming from nowhere and (...) deprived of any historicity and sociality), Quale’s argumentation becomes questionable. I illustrate this point of view by analysing his discourse concerning the role of language in the conceptualization of cognition and his attempt to ground the source of ethics in the individual construction of the world. (shrink)

In dealing with the radical politicization of psychoanalysis from a geopolitical standpoint, this essay argues that psychoanalysis has to be capable to rethink and reembody itself with every contingent and immanent dislocations of its transcendental horizons. Through a reading of Slavoj Žižek and Alain Badiou on Mao Tse-Tung, we can think about the notion of dislocation and localization of the Idea. We will argue that this has historically happened in psychoanalysis in the transition from Freud to Lacan; however, the issue (...) is that this dislocation has undergone a retroactivity of necessity which makes a vanishing mediator out of the contingent scrap of reality that it initially relied on—and this forms the quilting point of the contemporary Lacanian ideology. Through Gabriel Tupinambá›s _The Desire of Psychoanalysis_, we will inspect the notion of generic psychoanalysis. We will insist that while generic psychoanalysis is crucial for the refiguring of psychoanalytic politics in a dislocative matter, we need to take this outlook to the end onto a psychoanalysis that is willing to impurify itself through localization as this is the only psychoanalysis worthy of the name. (shrink)

Generic language (e.g., “tigers have stripes”) leads children to assume that the referenced category (e.g., tigers) is inductively informative and provides a causal explanation for the behavior of individual members. In two preregistered studies with 4- to 7-year-old children (N = 497), we considered the mechanisms underlying these effects by testing how correcting generics might affect the development of these beliefs about novel social and animal kinds (Study 1) and about gender (Study 2). Correcting generics by narrowing their scope (...) to a single individual limited beliefs that the referenced categories could explain what their members would be like while broadening the scope to a superordinate category (Study 2) uniquely limited endorsement of gender norms. Across both studies, correcting generics did not alter beliefs about feature heritability and had mixed effects on inductive inferences, suggesting that additional mechanisms (e.g., causal reasoning about shared features) contribute to the development of full-blown essentialist beliefs. These results help illuminate the mechanisms by which generics lead children to view categories as having rich inductive and causal potential; in particular, they suggest that children interpret generics as signals that speakers in their community view the referenced categories as meaningful kinds that support generalization. The findings also point the way to concrete suggestions for how adults can effectively correct problematic generics (e.g., gender stereotypes) that children may hear in daily life. (shrink)

I have taken the traditional problem of the seeming interdependence of identity concepts and essentialistic concepts and the attendant difficulties with circularity as a starting point in my consideration of recent attempts to provide accounts ofde re essences. Having distinguished between theories of individual and generic essences, I have shown how a linguistic device based upon a new approach to referring expressions has, perhaps, provided some advance in the understanding of individualde re essences. I have argued that, however (...) efficacious these linguistic devices may be in dealing with individual essences, they are of no help in dealing with generic essences. I considered, therefore, one of the recent attempts to use science as the arbiter ofde re essences and concluded that such attempts will not, ultimately, solve the traditional problem of circularity. That problem remains, arising in different forms to thwart different attempts to account forde re generic essences. (shrink)

Given a finitely generated group Γ, we study the space Isom(Γ, ℚ������) of all actions of Γ by isometries of the rational Urysohn metric space ℚ������, where Isom(Γ, ℚ������) is equipped with the topology it inherits seen as a closed subset of Isom(ℚ������) Γ . When Γ is the free group ������ n on n generators this space is just Isom(ℚ������) n , but is in general significantly more complicated. We prove that when Γ is finitely generated Abelian there is (...) a generic point in Isom(Γ, ℚ������), i.e., there is a comeagre set of mutually conjugate isometric actions of Γ on ℚ������. (shrink)

A look at history showed that theology always has to face contemporary demands in terms of its scientific character. At present, processes of pluralisation and secularisation challenge the existence of theology at universities not only against the background of religious studies, which are independent of the churches, but also, for example, in relation to innovative life sciences or cognitive sciences. In this context, an essential point to consider was that theology – like social systems in general and science in (...) particular – is characterised by an increasing differentiation. This differentiation of science implied an increasing specialisation of research, which could also be observed in the field of theology and its sub-disciplines. This article accordingly addressed the question of how, in the face of increasingly specialised research studies, the unity of theology can be justified beyond abstract and sweeping determinations. The present contribution suggested that in this respect a model of research designs developed in religious didactics might prove useful. This model of research design could essentially be understood as consisting of three research dimensions that define a research space, in which the research study on the didactics of religion can be located in the three-dimensional space by the research goal as a formatting factor. The three dimensions of this model, including the research goal, seemed to be broad enough to be tested in other sub-disciplines of theology as well to see whether their research can be more closely defined with them.Contribution: Accordingly, the contribution of this article was to raise the question, in view of an increasing specialisation of theological research, to what extent a model of research designs developed in the didactics of religion could be transferred to other sub-disciplines of theology. Should this succeed a new approach to justifying the unity of theology could become available, which is able to take into account the current differentiation of theology. (shrink)

Let G be a stable abelian group with regular modular generic. We show that either 1. there is a definable nongeneric K ≤ G such that G/K has definable connected component and so strongly regular generics, or 2. distinct elements of the division ring yielding the dependence relation are represented by subgroups of G × G realizing distinct strong types (when regarded as elements of G eq ). In the latter case one can choose almost 0-definable subgroups representing the (...) elements of the division ring. We find a bound $((G: G^0))$ for the size of the division ring in case G has no definable subgroup K so that G/K is infinite with definable connected component. We show in case (2) that the group G/H, where H consists of all nongeneric points of G, inherits a weakly minimal group structure from G naturally, and Th(G/H) is independent of the particular model G as long as G/H is infinite. (shrink)

Let be a countable first order structure and endow the universe of with the discrete topology. Then the automorphism group of becomes a topological group. A tuple of automorphisms is defined to be weakly generic iff its diagonal conjugacy class (in the algebraic sense) is dense (in the topological sense) and the ‐orbit of each is finite. Existence of tuples of weakly generic automorphisms are interesting from the point of view of model theory as well as from (...) the point of view of finite combinatorics.The main results of the present work are as follows. In Theorem 2.6 we characterize the existence of tuples of weakly generic automorphisms with the aid of the profinite topology of free groups. In Corollary 2.12 we will show that if has finite topological rank r (and satisfies a further, mild technical condition) then the existence of a weakly generic tuple in implies the existence of weakly generic tuples in for all natural number. Finally, in Theorem 3.2 we show that if is a countable model of an ℵ0‐categorical, simple theory in which all types over the empty set are stationary and has a pair of weakly generic automorphisms then it has tuples of weakly generic automorphisms of arbitrary finite length.At the technical level we will combine elementary investigations about the profinite topology of free groups with the results of [11] about topological ranks of the automorphism groups of some structures. (shrink)

We show that every nonzero $${\Delta^{0}_{2}}$$ enumeration degree bounds the enumeration degree of a 1-generic set. We also point out that the enumeration degrees of 1-generic sets, below the first jump, are not downwards closed, thus answering a question of Cooper.

PROBEX (PROBabilities from EXemplars), a model of probabilistic inference and probability judgment based on generic knowledge is presented. Its properties are that: (a) it provides an exemplar model satisfying bounded rationality; (b) it is a “lazy” algorithm that presumes no pre‐computed abstractions; (c) it implements a hybrid‐representation, similarity‐graded probability. We investigate the ecological rationality of PROBEX and find that it compares favorably with Take‐The‐Best and multiple regression (Gigerenzer, Todd, & the ABC Research Group, 1999). PROBEX is fitted to the (...) point estimates, decisions, and probability assessments by human participants. The best fit is obtained for a version that weights frequency heavily and retrieves only two exemplars. It is proposed that PROBEX implements speed and frugality in a psychologically plausible way. (shrink)

Ceteris Paribus (cp-)laws may be said to hold only ``other things equal,'' signaling that their truth is compatible with a range of exceptions. Several theorists have taken this feature to introduce the presumption that cp-laws are trivial, one that needs to be countered if we are to appeal to cp-laws in the course of scientific investigation or our philosophical theorizing about it. I argue that the triviality worry is misplaced by pointing out that cp-laws are just a subset of uncontroversially (...) meaningful and contingent expressions of natural language, the generics. I then present an account of these generics that elucidates some of their most puzzling features, especially the ones that suggested the triviality worry in the first place. (shrink)

It is known that there is a close relation between Prikry forcing and the iteration of ultrapowers: If U is a normal ultrafilter on a measurable cardinal κ and 〈Mn, jm,n | m ≤ n ≤ ω〉 is the iteration of ultrapowers of V by U, then the sequence of critical points 〈j0,n | n ∈ ω〉 is a Prikry generic sequence over Mω. In this paper we generalize this for normal precipitous filters.

We define the notion of a weakly pointed tree, and characterize the amount of genericity necessary to prevent a uniformly branching tree being weakly pointed. We use these ideas to show there is no topological analogue of a measure-theoretic selection theorem of Graf and Mauldin.

Probably the two most famous examples of elementary embeddings between inner models of set theory are the embeddings of the universe into an inner model given by a measurable cardinal and the embeddings of the constructible universeLinto itself given by 0#. In both of these examples, the “target model” is a subclass of the “ground model”. It is not hard to find examples of embeddings in which the target model is not a subclass of the ground model: ifis a (...) class='Hi'>generic ultrafilter arising from forcing with a precipitous ideal on a successor cardinalκ, then the ultraproduct of the ground model viacollapsesκ. Such considerations suggest a classification of how close the target model comes to “fitting inside” the ground model.Definition 1.1. LetMandNbe inner models of ZFC, and letj:M→Nbe an elementary embedding. Theco-critical pointofjis the least ordinalλ, if any exist, such that there isX⊆λ, X∈NbutX∉M. Such anXis called anew subsetofλ.It is easy to see that the co-critical point ofj:M→Nis a cardinal inN. (shrink)

The break necessary to establish a rigorous science of cultural works is something more and something else than a simple methodological reversal.1 It implies a true conversion of the ordinary way of thinking and living the intellectual enterprise. It is a matter of breaking the narcissistic relationship inscribed in the representation of intellectual work as a “creation” and which excludes as the expression par excellence of “reductionist sociology” the effort to subject the artist and the work of art to a (...) way of thinking that is doubly objectionable since it is both genetic and generic.It would be easy to show what the most different kinds of analysis of the work of art owe to the norms that require treating works in and for themselves, with no reference to the social conditions of their production. Thus in the now-classic Theory of Literature, René Wellek and Austin Warren seem to advocate “an explanation in terms of the personality and the life of the writer.” In fact, because they accept the ideology of the “man of genius” they are committed, in their own terms, to “one of the oldest and best-established methods of literary study”—which seeks the explanatory principle of a work in the author taken in isolation .2 In fact, this explanatory principle resides in the relationship between the “space” of works in which each particular work is taken and the “space” of authors in which each cultural enterprise is constituted. Similarly, when Sartre takes on the project of specifying the meditations through which society determined Flaubert, the individual, he attributes to those factors that can be perceived from that point of view—that is, to social class as refracted through a family structure—what are instead the effects of generic factors influencing every writer in an artistic field that is itself in a subordinate position in the field of power and also the effects specific to all writers who occupy the same position as Flaubert within the artistic field. 1. See Pierre Bourdieu, “Intellectual Field and Creative Project,” trans. Sian France, Social Science Information 8 : 89-119; originally published as “Champ intellectual et projet créateur,” Les Temps moderns no. 246 : 865-906. See also Bourdieu, “Champ du pouvoir, champ intellectual et habitus de classe,” Scolies 1 : 7-26, and Bourdieu, “The Genesis of the Concepts of Habitus and Field,” trans. Channa Newman, Sociocriticism no. 2 : 11-24.2. René Welleck and Austin Warren, Theory of Literature p. 69. Pierre Bourdieu holds the chair of sociology at the Collège de France and is director of the Centre de Sociologie européenne at the École des Hautes Études en Sciences Sociales. Among his most recent works are Distinction , Homo Academicus , and Choses Dites. (shrink)

The generic ultrafilter${\cal G}_2 $forced by${\cal P}\left/\left$was recently proved to be neither maximum nor minimum in the Tukey order of ultrafilters, but it was left open where exactly in the Tukey order it lies. We prove${\cal G}_2 $that is in fact Tukey minimal over its projected Ramsey ultrafilter. Furthermore, we prove that for each${\cal G}_2 $, the collection of all nonprincipal ultrafilters Tukey reducible to the generic ultrafilter${\cal G}_k $forced by${\cal P}\left/{\rm{Fin}}^{ \otimes k} $forms a chain of lengthk. (...) Essential to the proof is the extraction of a dense subsetεkfrom +which we prove to be a topological Ramsey space. The spacesεk,k≥ 2, form a hierarchy of high dimensional Ellentuck spaces. New Ramsey-classification theorems for equivalence relations on fronts on εkare proved, extending the Pudlák–Rödl Theorem for fronts on the Ellentuck space, which are applied to find the Tukey and Rudin–Keisler structures below${\cal G}_k $. (shrink)

Point-of-care evidence-based medicine websites allow physicians to answer clinical queries using recent evidence at the bedside. Despite significant research into the function, usability and effectiveness of these programmes, little attention has been paid to their ethical issues. As many of these sites summarise the literature and provide recommendations, we sought to assess the role of conflicts of interest in two widely used websites: UpToDate and Dynamed. We recorded all conflicts of interest for six articles detailing treatment for the following (...) conditions: erectile dysfunction, fibromyalgia, hypogonadism, psoriasis, rheumatoid arthritis and Crohn's disease. These diseases were chosen as their medical management is either controversial, or they are treated using biological drugs which are mostly available by brand name only. Thus, we hypothesised that the role of conflict of interest would be more significant in these conditions than in an illness treated with generic medications or by strict guidelines. All articles from the UpToDate articles demonstrated a conflict of interest. At times, the editor and author would have a financial relationship with a company whose drug was mentioned within the article. This is in contrast with articles on the Dynamed website, in which no author or editor had a documented conflict. We offer recommendations regarding the role of conflict of interest disclosure in these point-of-care evidence-based medicine websites. (shrink)

In 1920 Łukasiewicz published a two-page article whose title was “On Three-valued Logic”. The paper proposes a semantic characterization for the logic that has been later called Ł3 . In spite of the shortness of the paper, all the important points concerning the semantics of Ł3 are already there and can be naturally generalized to the case of a generic number n of truth-values . The conclusion of the article is quite interesting:The present author is of the opinion that (...) three-valued logic has above all theoretical importance as an endeavour to construct a system of non-aristotelian logic. Whether the new system of logic has any practical importance will be seen only when the logical phenomena, especially those in the deductive sciences, are thoroughly examined, and when the consequences of the indeterministic philosophy, which is the metaphysical substratum of the new logic, can be compared with empirical data. (shrink)

We study the expressive power in the finite of the logic Fixed-Point+Counting, the extension of first-order logic which is obtained through adding both the fixed-point constructor and the ability to count. To this end an isomorphism preserving (`generic') model of computation is introduced whose PTime restriction exactly corresponds to this level of expressive power, while its PSpace restriction corresponds to While+Counting. From this model we obtain a normal form which shows a rather clear separation of the relational (...) vs. the arithmetical side of the algorithms involved. In parallel, we study the relations of Fixed-Point+Counting with the infinitary logics L r ∞ω (∃ ≥ m ) m∈ω and the corresponding pebble games. The main result, however, involves the concept of an arithmetical invariant. By this we mean a functor taking every finite relational structure to an expansion of (an initial segment of) the standard arithmetical structure. In particular its values are linearly ordered structures. We establish the existence of a family of arithmetical invariants (J r ) r≥ 1 with the following properties: $\bullet$ The invariants themselves can be evaluated in polynomial time. $\bullet$ A class of finite relational structures is definable in Fixed-Point+Counting if and only if membership can be decided in polynomial time on the basis of the values of one of the invariants. $\bullet$ The invariant J r classifies all finite relational structures exactly up to equivalence with respect to the logic L r ∞ω (∃ ≥ m ) m∈ω . We also give a characterization of Fixed-Point+Counting in terms of sequences of formulae in the L r ωω (∃ ≥ m ) m∈ω : It corresponds exactly to the polynomial time computable families (φ n ) n∈ω in these logics. Towards a positive assessment of the expressive power of Fixed-Point+Counting, it is shown that the natural extension of fixed-point logic by Lindström quantifiers, which capture all the PTime computable properties of cardinalities of definable predicates, is strictly weaker than what we get here. This implies in particular that every extension of fixed-point logic by means of monadic Lindstrom quantifiers, which stays within PTime, must be strictly contained in Fixed-Point+Counting. (shrink)

The notion of a [Formula: see text]-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each [Formula: see text], any [Formula: see text]-generic sequence of P-points can be extended to an [Formula: see text]-generic sequence. This shows that the CH implies that there is a chain of P-points of length [Formula: see text] with respect to both Rudin–Keisler and Tukey reducibility. These results answer an old question of Andreas (...) Blass. (shrink)

We study extensions of Presburger arithmetic with a unary predicate R and we show that under certain conditions on R, R is sparse and the theory of $\langle\mathbb{N}, +, R\rangle$ is decidable. We axiomatize this theory and we show that in a reasonable language, it admits quantifier elimination. We obtain similar results for the structure $\langle\mathbb{Q},+, R\rangle$.

It is known today that Hegel's philosophy was at the center of the development of pragmatism. In particular, the relation of Dewey's philosophy to Hegel's has recently been studied with great attention1. Many studies have revealed that the German philosopher had a fundamental influence on the young John Dewey, particularly with regard to his theory of culture, for his logic, as well as for his psychology. These new readings propose a profoundly original view of Dewey and explain why he thought (...) of his philosophy as a "permanent Hegelian deposit".Our work aims to... (shrink)

This corrigendum concerns [, § ] on ordered difference existentially closed valued fields where we overlooked the problem of immediate extensions.

An elliptic curve over a supersimple field with exactly one extension of degree 2 has an s-generic point.