We give some general criteria for the stable embeddedness of a definable set. We use these criteria to establish the stable embeddedness in algebraically closed valued fields of two definable sets: The set of balls of a given radius r < 1 contained in the valuation ring and the set of balls of a given multiplicative radius r < 1. We also show that in an algebraically closed valued field a 0-definable set is stably embedded if and only if its (...) algebraic closure is stably embedded. (shrink)

Reviewed Works:B. I. Zil'ber, L. Pacholski, J. Wierzejewski, A. J. Wilkie, Totally Categorical Theories: Structural Properties and the Non-Finite Axiomatizability.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. II.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. III.B. I. Zil'ber, E. Mendelson, Totally Categorical Structures and Combinatorial Geometries.B. I. Zil'ber, The Structure of Models of Uncountably Categorical Theories.

We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups (...) and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups. (shrink)

A set of axioms is presented defining an ‘analytic Zariski structure’, as a generalisation of Hrushovski and Zilber’s Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski’s method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of ‘quasi-analytic’ results are derived for this example e.g. analogues of Chow’s theorem and the proper mapping theorem.

We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties.

A first order theory T of power λ is called unidimensional if any twoλ+-saturated models of T of the same cardinality are isomorphic. We prove here that such theories are superstable, solving a problem of Shelah. The proof involves an existence theorem and a definability theorem for definable groups in stable theories, and an analysis of their relation to regular types.

We attempt to formulate issues around modularity and Zilber’s trichotomy in a setting that intersects additive combinatorics. In particular, we update the open problems on quasi-finite structures from [9].

Using methods of geometric stability , we determine the structure of Abelian groups definable in ACFA, the model companion of fields with an automorphism. We also give general bounds on sets definable in ACFA. We show that these tools can be used to study torsion points on Abelian varieties; among other results, we deduce a fairly general case of a conjecture of Tate and Voloch on p-adic distances of torsion points from subvarieties.

Kueker's conjecture is proved for stable theories, for theories that interpret a linear ordering, and for theories with Skolem functions. The proof of the stable case involves certain results on coordinatization that are of independent interest.

We prove (Proposition 2.1) that if $\mu$ is a generically stable measure in an NIP (no independence property) theory, and $\mu(\phi(x,b))=0$ for all $b$ , then for some $n$ , $\mu^{(n)}(\exists y(\phi(x_{1},y)\wedge \cdots \wedge\phi(x_{n},y)))=0$ . As a consequence we show (Proposition 3.2) that if $G$ is a definable group with fsg (finitely satisfiable generics) in an NIP theory, and $X$ is a definable subset of $G$ , then $X$ is generic if and only if every translate of $X$ does not (...) fork over $\emptyset$ , precisely as in stable groups, answering positively an earlier problem posed by the first two authors. (shrink)

We use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.

Finitely axiomatizable ℵ 1 categorical theories are locally modular.

A stable theory is finitely based if every set of indiscernibles is based on a finite subset. This is a common generalization of superstability and 1-basedness. We show that if such theories have more than one model they must have infinitely many, and prove some other conjectures.

Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.

We give several characterizations of weakly minimal abelian structures. In two special cases, dual in a sense to be made explicit below, we give precise structure theorems: 1. When the only finite 0-definable subgroup is {0}, or equivalently 0 is the only algebraic element (the co-strongly minimal case); 2. When the theory of the structure is strongly minimal. In the first case, we identify the abelian structure as a "near-subspace" A of a vector space V over a division ring D (...) with its induced structure, with possibly some collection of distinguished subgroups of A of finite index in A and (up to $acl(\emptyset)$ ) no further structure. In the second, the structure is that of V/A for a vector space and near-subspace as above, with the only further possible structure some collection of distinguished points. Here a near-subspace of V is a subgroup A such that for any nonzero d ∈ D, the index of $A\cap dA$ in A is finite. We also show that any weakly minimal abelian structure is a reduct of a weakly minimal module. (shrink)

We study the automorphism group of the algebraic closure of a substructure A of a pseudofinite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the theory of pseudofinite fields, we show that over A, algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field.

We give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the ‘geometric' sorts which suffice to code all imaginaries in the corresponding algebraic setting.

We are concerned with identifying by how much a finite cover of an 0-categorical structure differs from a sequence of free covers. The main results show that this is measured by automorphism groups which are nilpotent-by-abelian. In the language of covers, these results say that every finite cover can be decomposed naturally into linked, superlinked and free covers. The superlinked covers arise from covers over a different base, and to describe this properly we introduce the notion of a quasi-cover.These results (...) generalise results of the second author obtained in the case where the base of the cover is a grassmannian of a disintegrated set. They also give a complete proof of a statement of the second author extending this case to the case of a grassmannian of a modular set. To do this, we need to analyse the possible superlinked covers of such a set.We also give a combinatorial condition on the base of a cover which guarantees various chain conditions on finite covers over this base, and introduce a pregeometry which is useful in the analysis of finite covers with simple fibre groups. (shrink)

We construct a strongly minimal set which is not a finite cover of one with DMP. We also show that for a strongly minimal theory T, generic automorphisms exist iff T has DMP, thus proving a conjecture of Kikyo and Pillay.

Ne estas prima orda formulo, kiu definas la Zariskijajn slositojn inter la konstruitoj, malpli ke la konektojn inter la slositoj.

This theory accords to volitions the status of basic mental actions, maintaining that these are spontaneous exercises of the will--a "two-way" power which ...

Durkheim écrit ce livre avec un but double : d'abord il voulait expliquer ce qui crée une société, ce qui la tient ensemble ; ensuite il voulait éclaircir l'influence qu'a la société sur la pensée logique. Pour Durkheim, la religion est la clé utilisée pour déverrouiller ces deux problématiques.Dans ce livre, Durkheim argumente que les représentations religieuses sont en fait des représentations collectives : l'essence du religieux ne peut être que le sacré. Il est une caractéristique qui se trouve universellement (...) dans toutes les religions. Le sacré, être collectif et impersonnel, représente ainsi la société elle-même. Ensuite il argumente que la société a un impact majeur dans la genèse de la pensée logique. C'est la société qui fournit à l'individu les catégories (le temps, l'espace, le nombre etc.) et les concepts nécessaires pour la pensée logique. (shrink)

There is a long tradition in philosophy and literary theory defending the view that engagement with literature promotes readers’ empathy. Until the last century, few of the empirical claims adduced in that tradition were investigated experimentally. Recent work in psychology and neuropsychology has now shed new light on the interplay of empathy and literature. This article surveys the experimental findings, addressing three central questions: What is it to read empathically? Does reading make us more empathic? What characteristics of literature, if (...) any, affect readers’ empathy? While experimental studies have delivered no conclusive answers to these questions, it has exposed their psychological complexity and constructed a more nuanced picture of the diverse ways in which literature interacts with our empathic capacities. (shrink)

The Spinoza party -- The Tractatus Theologico-Politicus: a democratic manifesto -- The Tractatus Politicus: a science of the state -- The Ethics: a political anthropology -- Politics and communication.

Издание содержит: хрестоматия; философы; психологи; литературоведы, искусствоведы; мастер изобразительного искусства и др.

With special emphasis on Foucault's many recently published lecture series this book provides an updated, comprehensive presentation of his most important diagnoses, his many ground-breaking analytical concepts as well as a systematic account of his unique conception of philosophy.

When we perceive an object, we perceive the object from a perspective. As a consequence of the perspectival nature of perception, when we perceive, say, a circular coin from different angles, there is a respect in which the coin looks circular throughout, but also a respect in which the coin's appearance changes. More generally, perception of shape and size properties has both a constant aspect—an aspect that remains stable across changes in perspective—and a perspectival aspect—an aspect that changes depending on (...) one's perspective on the object. How should we account for the perspectival aspect of spatial perception? We present a framework within which to discuss the perspectival aspect of perception and put forward three desiderata that any account of the perspectival aspect of perception should satisfy. We discuss views on which the perspectival aspect of perception is analyzed in terms of constitutively mind-dependent appearance properties as well as views on which the perspectival aspect of perception is analyzed in terms of representations of mind-independent perspectival properties. (shrink)

First published in 1818, The World as Will and Representation contains Schopenhauer's entire philosophy, ranging through epistemology, metaphysics, philosophy of mind and action, aesthetics and philosophy of art, to ethics, the meaning of life and the philosophy of religion, in an attempt to account for the world in all its significant aspects. It gives a unique and influential account of what is and is not of value in existence, the striving and pain of the human condition and the possibility of (...) deliverance from it. This new translation of the first volume of what later became a two-volume work reflects the eloquence and power of Schopenhauer's prose and renders philosophical terms accurately and consistently. It offers an introduction, glossary of names and bibliography, and succinct editorial notes, including notes on the revisions of the text which Schopenhauer made in 1844 and 1859. (shrink)

We argue that the trend toward providing users with feasible and actionable explanations of AI decisions—known as recourse explanations—comes with ethical downsides. Specifically, we argue that recourse explanations face several conceptual pitfalls and can lead to problematic explanation hacking, which undermines their ethical status. As an alternative, we advocate that explanations of AI decisions should aim at understanding.