It follows directly from Shelah’s structure theory that if T is a classifiable theory, then the isomorphism type of any model of T is determined by the theory of that model in the language L∞,ω1. Leo Harrington asked if one could improve this to the logic L∞, In [S. Shelah, Characterizing an -saturated model of superstable NDOP theories by its L∞,-theory, Israel Journal of Mathematics 140 61–111] Shelah gives a partial positive answer, showing that for T a countable superstable NDOP (...) theory, two -saturated models of T are isomorphic if and only if they have the same L∞,-theory. We give here a negative answer to the general question by constructing two classifiable theories, each with 21 pairwise non-isomorphic models of cardinality 1, which are all L∞,-equivalent, a shallow depth 3 ω-stable theory and a shallow NOTOP depth 1 superstable theory. In the other direction, we show that in the case of an ω-stable depth 2 theory, the L∞,-theory is enough to describe the isomorphism type of all models. (shrink)

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)

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.

In [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. (N.S.) 19(4) (2013) 865–877], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that [Formula: see text] has the canonical base property in a strong form; “internality to” being replaced by “algebraicity in”. In the current paper, we give a reasonably robust definition of the “strong canonical base property” in a rather more general finite (...) rank context than [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. (N.S.) 19(4) (2013) 865–877], and prove its equivalence with rigidity of the relevant definable Galois groups. The new direction is an elaboration on the old result that [Formula: see text]-based groups are rigid. (shrink)

We present a self-contained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah's 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. The exposition is from a contemporary perspective and takes into account contributions due to S. Buechler, E. Hrushovski, B. Kim, O. Lessmann, S. Shelah and A. Pillay.

In this paper, we introduce an AEC framework for studying fields with commuting automorphisms. Fields with commuting automorphisms are closely related to difference fields. Some authors define a difference ring (or field) as a ring (or field) together with several commuting endomorphisms, while others only study one endomorphism. Z. Chatzidakis and E. Hrushovski have studied in depth the model theory of ACFA, the model companion of difference fields with one automorphism. Our fields with commuting automorphisms generalize this setting. We (...) have several automorphisms and they are required to commute. Hrushovski has proved that in the case of fields with two or more commuting automorphisms, the existentially closed models do not necessarily form a first order model class. In the present paper, we introduce FCA-classes, an AEC framework for studying the existentially closed models of the theory of fields with commuting automorphisms. We prove that an FCA-class has AP and JEP and thus a monster model, that Galois types coincide with existential types in existentially closed models, that the class is homogeneous, and that there is a version of type amalgamation theorem that allows to combine three types under certain conditions. Finally, we use these results to show that our monster model is a simple homogeneous structure in the sense of S. Buechler and O. Lessman (this is a non-elementary analogue for the classification theoretic notion of a simple first order theory). (shrink)

Generalising Hrushovski's fusion technique we construct the free fusion of two strongly minimal theories T₁, T₂ intersecting in a totally categorical sub-theory T₀. We show that if, e.g., T₀ is the theory of infinite vector spaces over a finite field then the fusion theory Tω exists, is complete and ω-stable of rank ω. We give a detailed geometrical analysis of Tω, proving that if both T₁, T₂ are 1-based then, Tω can be collapsed into a strongly minimal theory, if (...) some additional technical conditions hold—all trivially satisfied if T₀ is the theory of infinite vector spaces over a finite field Fq. (shrink)

Model theory is concerned mainly, although not exclusively, with infinite structures. In recent years, finite structures have risen to greater prominence, both within the context of mainstream model theory, e.g., in work of Lachlan, Cherlin, Hrushovski, and others, and with the advent of finite model theory, which incorporates elements of classical model theory, combinatorics, and complexity theory. The purpose of this survey is to provide an overview of what might be called the model theory of finite structures. Some topics (...) in finite model theory have strong connections to theoretical computer science, especially descriptive complexity theory. In fact, it has been suggested that finite model theory really is, or should be, logic for computer science. These connections with computer science will, however, not be treated here.It is well-known that many classical results of ‘infinite model theory’ fail over the class of finite structures, including the compactness and completeness theorems, as well as many preservation and interpolation theorems. The failure of compactness in the finite, in particular, means that the standard proofs of many theorems are no longer valid in this context. At present, there is no known example of a classical theorem that remains true over finite structures, yet must be proved by substantially different methods. It is generally concluded that first-order logic is ‘badly behaved’ over finite structures.From the perspective of expressive power, first-order logic also behaves badly: it is both too weak and too strong. Too weak because many natural properties, such as the size of a structure being even or a graph being connected, cannot be defined by a single sentence. Too strong, because every class of finite structures with a finite signature can be defined by an infinite set of sentences. Even worse, every finite structure is defined up to isomorphism by a single sentence. In fact, it is perhaps because of this last point more than anything else that model theorists have not been very interested in finite structures. Modern model theory is concerned largely with complete first-order theories, which are completely trivial here. (shrink)

We propose a criterion to regard a property of a theory (in first or second order logic) as virtuous: the property must have significant mathematical consequences for the theory (or its models). We then rehearse results of Ajtai, Marek, Magidor, H. Friedman and Solovay to argue that for second order logic, ‘categoricity’ has little virtue. For first order logic, categoricity is trivial; but ‘categoricity in power’ has enormous structural consequences for any of the theories satisfying it. The stability hierarchy extends (...) this virtue to other complete theories. The interaction of model theory and traditional mathematics is examined by considering the views of such as Bourbaki, Hrushovski, Kazhdan, and Shelah to flesh out the argument that the main impact of formal methods on mathematics is using formal definability to obtain results in ‘mainstream’ mathematics. Moreover, these methods (e.g., the stability hierarchy) provide an organization for much mathematics which gives specific content to dreams of Bourbaki about the architecture of mathematics. (shrink)

Several attempts have been done to distinguish “positive” information in an arbitrary first order theory, i.e., to find a well behaved class of closed sets among the definable sets. In many cases, a definable set is said to be closed if its conjugates are sufficiently distinct from each other. Each such definition yields a class of theories, namely those where all definable sets are constructible, i.e., boolean combinations of closed sets. Here are some examples, ordered by strength:Weak normality describes a (...) rather small class of theories which are well understood by now (see, for example, [P]). On the other hand, normalization is so weak that all theories, in a suitable context, are normalizable (see [HH]). Thus equational theories form an interesting intermediate class of theories. Little work has been done so far. The original work of Srour [S1, S2, S3] adopts a point of view that is closer to universal algebra than to stability theory. The fundamental definitions and model theoretic properties can be found in [PS], though some easy observations are missing there. Hrushovski's example of a stable non-equational theory, the first and only one so far, is described in the unfortunately unpublished manuscript [HS]. In fact, it is an expansion of the free pseudospace constructed independently by Baudisch and Pillay in [BP] as an example of a strictly 2-ample theory. Strong equationality, defined in [Hr], is also investigated in [HS]. (shrink)

Generalizedn-gons are certain geometric structures (incidence geometries) that generalize the concept of projective planes (the nontrivial generalized 3-gons are exactly the projective planes).In a simplified world, every generalizedn-gon of finite Morley rank would be an algebraic one, i.e., one of the three families described in [9] for example. To our horror, John Baldwin [2], using methods discovered by Hrushovski [7], constructed ℵ1-categorical projective planes which are not algebraic. The projective planes that Baldwin constructed fail to be algebraic in a (...) dramatic way.Indeed, every algebraic projective plane over an algebraically closed field is Desarguesian [12]. In particular, an algebraically closed field (isomorphic to the base field) can be interpreted in every one of them. However, in the projective planes that Baldwin constructed, one cannot even interpret an infinite group.In this article we show that the same phenomenon occurs for the generalizedn-gons ifn≥ 3 is an odd integer. For each suchnwe constructmany nonisomorphic generalizedn-gons of finite Morley rank that do not interpret an infinite group. As one may expect, our method is inspired by Hrushovski and Baldwin, and we follow Baldwin's line of approach. Quite often our proofs are a verification of the fact that the proofs of Baldwin [2] forn= 3 carry over to an arbitrary positive odd integern(which is sometimes far from being obvious). As in [2], we begin by defining a certain collection of finite graphsK* and a binary relation ≤ on these graphs. We show that (K*, ≤) satisfies the amalgamation property. (shrink)

We consider${\cal S}$, the class of finite semilattices;${\cal T}$, the class of finite treeable semilattices; and${{\cal T}_m}$, the subclass of${\cal T}$which contains trees with branching bounded bym. We prove that${\cal E}{\cal S}$, the class of finite lattices with linear extensions, is a Ramsey class. We calculate Ramsey degrees for structures in${\cal S}$,${\cal T}$, and${{\cal T}_m}$. In addition to this we give a topological interpretation of our results and we apply our result to canonization of linear orderings on finite semilattices. In (...) particular, we give an example of a Fraïssé class${\cal K}$which is not a Hrushovski class, and for which the automorphism group of the Fraïssé limit of${\cal K}$is not extremely amenable but is uniquely ergodic. (shrink)

In this paper, I want to focus on the claim, prominently made by sensorimotor theorists, that perception is something we do. I will argue that understanding perceiving as a bodily doing allows for a strong non-dualistic position on the relation between experience and objective physical events, one which provides insight into why such relation seems problematic while at the same time providing means to relieve the tension. Next I will show how the claim that perception is something we do does (...) not stand in opposition to, and is not refuted by, the fact that we often have perceptual experience without moving. In arguing that cases of motionless perception and perception-like experience are still doings it will be pointed out that the same interactive regularities which are engaged in in active perception still apply to them. Explaining how past interactive regularities can influence current perception or perception-like experience in a way which remains true to the idea that perception is a doing, so I will argue, can be done by invoking the past -- the past itself, however, not its representation. The resulting historical, non-representational sensorimotor approach can join forces with Gibsonian ecological psychology -- provided that such is also understood along lines that don't invoke externalist remnants of contents. (shrink)

Measuring event-related potentials (ERPs) has been fundamental to our understanding of how language is encoded in the brain. One particular ERP response, the N400 response, has been especially influential as an index of lexical and semantic processing. However, there remains a lack of consensus on the interpretation of this component. Resolving this issue has important consequences for neural models of language comprehension. Here we show that evidence bearing on where the N400 response is generated provides key insights into what it (...) reflects. A neuroanatomical model of semantic processing is used as a guide to interpret the pattern of activated regions in functional MRI, magnetoencephalography and intracranial recordings that are associated with contextual semantic manipulations that lead to N400 effects. (shrink)

The thesis pseudofinite structures and counting dimensions is about the model theory of pseudofinite structures with the focus on groups and fields. The aim is to deepen our understanding of how pseudofinite counting dimensions can interact with the algebraic properties of underlying structures and how we could classify certain classes of structures according to their counting dimensions. Our approach is by studying examples. We treat three classes of structures: The first one is the class of H-structures, which are generic expansions (...) of existing structures. We give an explicit construction of pseudofinite H-structures as ultraproducts of finite structures. The second one is the class of finite difference fields. We study properties of coarse pseudofinite dimension in this class, show that it is definable and integer-valued and build a partial connection between this dimension and transformal transcendence degree. The third example is the class of pseudofinite primitive permutation groups. We generalise Hrushovski’s classical classification theorem for stable permutation groups acting on a strongly minimal set to the case where there exists an abstract notion of dimension, which includes both the classical model theoretic ranks and pseudofinite counting dimensions. In this thesis, we also generalise Schlichting’s theorem for groups to the case of approximate subgroups with a notion of commensurability.prepared by Tingxiang Zou.E-mail: [email protected]: https://tel.archives-ouvertes.fr/tel-02283810/document. (shrink)

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)

Cet article est un nouvel examen des objections soulevées par Leibniz dans la controverse avec Clarke contre la théorie absolutiste de l'espace et du temps. Or la plupart de ces objections sont fondées sur le principe de raison suffisante; mais Leibniz utilise aussi le principe de l'identité des indiscernables, qu'il prétend déduire du principe de raison suffisante . Ce qui m'intéresse c'est que Leibniz présente parfois deux versions de la même objection: l'une reposant uniquement sur le principe de raison suffisante, (...) l'autre uniquement sur le principe de l'identité des indiscernables. Se pose alors la question suivante: Leibniz aurait-il pu soulever toutes les objections qu'il voulait contre la théorie absolutiste, en utilisant seulement le principe de l'identité des indiscernables? Il me semble qu'il aurait certainement pu le faire. Et de plus, je crois que si Leibniz avait suivi cette voie, son raisonnement contre la théorie absolutiste aurait été beaucoup plus convaincant. Ainsi donc, je me propose de mener l'attaque de Leibniz contre la théorie absolutiste, en isolant, reformulant, et exposant systématiquement sept arguments dont il se servait ou dont il aurait pu se servir, qui sont tous fondés sur le principe de l'identité des indiscernables. (shrink)

Part four of the Proceedings of the fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada, August 27-September 2, 1975.

Because corporate social responsibility (CSR) is potentially beneficial for companies, it is important to understand the factors that improve a company’s CSR practice. Scholars hypothesize that facilitating learning organization characteristics, which are divided in characteristics at the organizational and the operational level, may improve CSR implementation. These characteristics stimulate companies and their members to be critical, learn from the past, and embrace change, but there is limited empirical evidence of this approach. This study addresses this gap by surveying 280 CSR (...) professionals and performing bootstrap mediation analyses to test multiple hypotheses. Learning organization characteristics at the organizational level, play a key role in supporting CSR implementation: leadership for learning, system connection, and group learning show a direct relationship with CSR implementation. It is striking that the role of the learning organization characteristics at the operational level is only indirect; the organizational characteristics mediate their relationship with CSR implementation. (shrink)

Este ensaio pretende levantar as seguintes questões: 1. de que modo é possível reconstituir o sentido de moral segundo um amor-próprio cujo conteúdo é dado menos por um isolamento ou negaçáo do outro do que por um trabalho pessoal sobre si mesmo, em vista de um êthos , de uma ética? 2. em que medida o valor da moral hoje em dia pode ser deslocado da lei universal para uma atitude de diferença, da normalidade do comportamento para o cultivo de (...) si e, por fim, da verdade sobre o sujeito para uma subjetivaçáo ascética que náo exige a prerrogativa de uma identidade, mas a transformaçáo de si na relaçáo consigo e com os outros? Tais questões sáo levantadas a partir de Friedrich Nietzsche, Michel Foucault e Fernando Savater. Palavras-chave: Amor-próprio, Estética da existência, Ética, Identidade. (shrink)

The public expects members of the medical profession to conduct themselves according to the terms of the Hippocratic oath, yet few physicians and virtually no laypersons know what is in that oath. For the oath to reach beyond its symbolic importance, ethical conduct must be learned and practised. There are many texts on the practice of medicine, surgery and all of the related disciplines, yet one is hard pressed to find anything on ethical practice in any of them. Scholarly texts (...) on ethics tend to deal with the landmark issues and dilemmas that have occurred within particular jurisdictions or religions. This book is intended as a student-friendly text that seeks not to turn students into ethics scholars but to provide them with a practical guide to ethical conduct in everyday medical practice. and discussion are provided for each of the following areas: Ethical Practices in Health Care Law and Ethics Rights of Patients and Responsibilities of Health-Care Providers The Rights of Health-Care Professionals The Duty of Care Confidentiality Consent to Treatment Life and Death Research Ethics Ethics in Public Health Practice Ethical Practice in Everyday Health Care is useful, practical and student friendly. The exercises and discussions will stimulate thought about ethical conduct and help students to develop and translate ethical principles into their daily practice as health-care workers. Dr Walrond offers a ready and concise source of information for medical students on ethical issues. The text is simple, comprehensive and factual, addressing issues encountered in everyday medical practices. Case studies provide practical illustrations of complex ethical issues. (shrink)

Research papers presented at the same title scientific conference, dedicated to the World Philosophy Day.

This book is a lucid and readable account of Spinoza, Hume, Kant, Nietzsche, James, and Santayana, not only as contributors to present-day secularism, but as precursors of religious liberalism. Beck traces the theme of "secularism and human values" through these thinkers, though difficulties arise from the fact that they represent a radical divergence of philosophic interests, and in any case would hardly have recognized, much less defended, the particular variety of secularism and religious liberalism that has arisen in recent times, (...) and with which the author associates them.—T. E. V. (shrink)