Louveau, A., S. Shelah and B. Velikovi, Borel partitions of infinite subtrees of a perfect tree, Annals of Pure and Applied Logic 63 271–281. We define a notion of type of a perfect tree and show that, for any given type τ, if the set of all subtrees of a given perfect tree T which have type τ is partitioned into two Borel classes then there is a perfect subtree S of T such that all subtrees of S of (...) type τ belong to the same class. This result simultaneously generalizes the partition theorems of Galvin-Prikry and Galvin-Blass. The key ingredient of the proof is the theorem of Halpern-Laüchli on partitions of products of perfect trees. (shrink)

This paper develops the foundations of the descriptive set theory of countable Borel equivalence relations on Polish spaces with particular emphasis on the study of hyperfinite, amenable, treeable and universal equivalence relations.

Depuis le XIXe siècle et jusqu’à nos jours, l’expansion des activités physiques et sportives s’est accompagnée de différences et d’inégalités sociales. A fortiori parmi l’ensemble des femmes, rarement pensé comme étant un ensemble lui-même divisé et hiérarchisé. S’agissant de l’accès aux loisirs sportifs puis au sport, les rapports au temps et à toutes les formes de travail, les rapports au corps sont particulièrement différenciateurs pour elles. Jusqu’à la moitié du XXe siècle environ, le sport ne concerne, au regard des millions (...) de femmes paysannes, ouvrières et petites employées, qu’une minorité d’aristocrates, de mondaines puis de jeunes femmes cultivées. Nombre d’institutions (le mouvement olympique, le sport ouvrier, les fédérations existantes) s’opposeront au développement de ces activités pour celles qui demeurent avant tout des mères destinées au foyer. La massification du sport ces dernières décennies s’accompagne d’une persistance des inégalités parmi les femmes, y compris parmi les plus jeunes. (shrink)

We prove two results about the embeddability relation between Borel linear orders: For $\eta$ a countable ordinal, let $2^\eta$ (resp. $2^{<\eta}$) be the set of sequences of zeros and ones of length $\eta$ (resp. $<\eta$), equipped with the lexicographic ordering. Given a Borel linear order $X$ and a countable ordinal $\xi$, we prove the following two facts. (a) Either $X$ can be embedded (in a $\triangle^1_1(X,\xi)$ way) in $2^{\omega\xi}$, or $2^{\omega\xi + 1}$ continuously embeds in $X$. (b) Either $X$ can (...) embedded (in a $\triangle^1_1(X,\xi)$ way) in $2^{\omega\xi}$, or $2^{\omega\xi}$ continuously embeds in $X$. These results extend previous work of Harrington, Shelah and Marker. (shrink)

Sport makes it possible to (re)invest certain forms of capital which have been forged in and through professional work. Certain men thus manage to transfer their labour potential and their « pain threshold» to boxing or to rugby, while others invest their cultural capital in sports which involve forms of scientific knowledge. Bodies are not however gender-neutral. Men and women are thus set apart in the work of sport, both in its practice and in its normative representation. « Femininity » (...) has the prerogative of grace and beauty, in gymnastics or in skating, while masculinity and virility are signified in terms of broad shoulders, courage, the willingness to fight on. The cult of the body, which has remained in vogue since the 1980s, has to some extent blurred the boundaries between the sexes. Muscles have thus become emblematic of an all-purpose fitness. Despite this, the indifference of the media to numerous leading women athletes, along with the suspicions hanging over them of a blurred gender identity demonstrate that the muscular woman has failed to become an ideal of feminine beauty. While there are many different spaces within which fit bodies can be made profitable, those of women cyclists and football players, who stir up a certain gender trouble, do not occupy such spaces. (shrink)

The 2005 Avignon Theatre Festival sparked a vast controversy about the insistent presence of bodies (whether wounded, broken, or humiliated) on stage. Without subscribing to the reactionary critical response to the Festival, it is legitimate to return to the debate in order to question the ubiquity of the “victim body” in contemporary theatre. Such representations, far from being heterodox, are in fact part of the massive ideology of “the ethical”, as diagnosed by Alain Badiou. The oppressed body thus tends to (...) be assimilated to the body of the victim. The result is the obliteration of the resistance of subjects to their oppression, or of their active response to it, theatre being reduced to the maxims of a democratic materialism: “there are only bodies and languages”. (shrink)

We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially Π03 iff the invariants are countable sets of reals, it is potentially Π04 iff the invariants are countable sets of countable sets of reals, and so on. The proofs (...) use various techniques, including Vaught transforms, changing topologies, and the Scott analysis of countable models. (shrink)

The research presented in this paper was motivated by our aim to study a problem due to J. Bourgain [3]. The problem in question concerns the uniform boundedness of the classical separation rank of the elements of a separable compact set of the first Baire class. In the sequel we shall refer to these sets (separable or non-separable) as Rosenthal compacta and we shall denote by ∝(f) the separation rank of a real-valued functionfinB1(X), withXa Polish space. Notice that in [3], (...) Bourgain has provided a positive answer to this problem in the case ofKsatisfyingwithXa compact metric space. The key ingredient in Bourgain's approach is that whenever a sequence of continuous functions pointwise converges to a functionf, then the possible discontinuities of the limit function reflect a local ℓ1-structure to the sequence (fn)n. More precisely the complexity of this ℓ1-structure increases as the complexity of the discontinuities offdoes. This fruitful idea was extensively studied by several authors (c.f. [5], [7], [8]) and for an exposition of the related results we refer to [1]. It is worth mentioning that A.S. Kechris and A. Louveau have invented the rank rND(f) which permits the link between thec0-structure of a sequence (fn)nof uniformly bounded continuous functions and the discontinuities of its pointwise limit. Rosenthal'sc0-theorem [11] and thec0-index theorem [2] are consequences of this interaction.Passing to the case where either (fn)nare not continuous orXis a non-compact Polish space, this nice interaction is completely lost. (shrink)

Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class $$\Gamma $$, then its $$\Gamma $$ -code can be obtained from its Borel code in a hyperarithmetical manner. We extend Louveau’s theorem to Borel functions: If a Borel function on a Polish space happens to be a $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -function, then one can find its $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -code hyperarithmetically relative to its Borel code. More generally, (...) we prove extension-type, domination-type, and decomposition-type variants of Louveau’s theorem for Borel functions. (shrink)

We give positive answers to two open questions from [15]. (1) For every set C countably determined over A, if C is Π 0 α (Σ 0 α ) then it must be Π 0 α (Σ 0 α ) over A, and (2) every Borel subset of the product of two internal sets X and Y all of whose vertical sections are Π 0 α (Σ 0 α ) can be represented as an intersection (union) of Borel sets with (...) vertical sections of lower Borel rank. We in fact show that (2) is a consequence of the analogous result in the case when X is a measurable space and Y a complete separable metric space (Polish space) which was proved by A. Louveau and that (1) is equivalent to the property shared by the inverse standard part map in Polish spaces of preserving almost all levels of the Borel hierarchy. (shrink)

We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in R ω , with the lexicographic ordering. For Borel orders embeddable in R 2 , our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some $\mathbf{R}^n, n , and hyperprojective determinacy for the general case.

A number of results have been obtained concerning Borel structures starting with Silver and Friedman followed by Harrington, Shelah, Marker, and Louveau. Friedman also initiated the model theory of Borel (in fact totally Borel) structures. By this we mean the study of the class of Borel models of a given first-order theory. The subject was further investigated by Steinhorn. The present work is meant to go further in this direction. It is based on the assumption that the study of (...) the class of, say, countable models of a theory reduces to analyzing a single $\omega_1$-saturated model. The question then arises as to when such a model can be totally Borel. We present here a partial answer to this problem when the theory under investigation is superstable. (shrink)

We prove that there is a -ideal of compact sets which is strictly above in the Tukey order. Here is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veličković asked in [Alain Louveau, Boban Veličković, Analytic ideals and cofinal types, Ann. Pure Appl. Logic 99 171–195].

In the past thirty years, two fundamental issues have emerged in the philosophy of science. One concerns the appropriate attitude we should take towards scientific theories--whether we should regard them as true or merely empirically adequate, for example. The other concerns the nature of scientific theories and models and how these might best be represented. In this ambitious book, da Costa and French bring these two issues together by arguing that theories and models should be regarded as partially rather than (...) wholly true. They adopt a framework that sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate. The new machinery of "partial structures" that they develop offers a new perspective from which to view the nature of scientific models and their heuristic development. Their conclusions will be of wide interest to philosophers and historians of science. (shrink)

The Problem of Perception offers two arguments against direct realism--one concerning illusion, and one concerning hallucination--that no current theory of ...

In this paper I examine Grace A. de Laguna’s theory of universals in its historical context and in relation to contemporary debates in analytic metaphysics. I explain the central features of her theory, arguing that her theory should be classified as a form of immanent realism and as a powers ontology. I then show in what ways her theory affords a theory of modality in terms of potentialities and discuss some of its consequences along the way.

A. H. Louie's More Than Life Itself is an exploratory journey in relational biology, a study of life in terms of the organization of entailment relations in living systems. This book represents a synergy of the mathematical theories of categories, lattices, and modelling, and the result is a synthetic biology that provides a characterization of life. Biology extends physics. Life is not a specialization of mechanism, but an expansive generalization of it. Organisms and machines share some common features, but organisms (...) are not machines. Life is defined by a relational closure that places it beyond the reach of physicochemical and mechanistic dogma, outside the reductionistic universe, and into the realm of impredicativity. Function dictates structure. Complexity brings forth living beings. (shrink)

This companion is a cutting-edge primer to critical forms of the posthumanities and the feminist posthumanities, aimed at students and researchers who want to catch up with the recent theoretical developments in various fields in the humanities, such as new media studies, gender studies, cultural studies, science and technology studies, human animal studies, postcolonial critique, philosophy and environmental humanities. It contains a collection of nineteen new and original short chapters introducing influential concepts, ideas and approaches that have shaped and developed (...) new materialism, inhuman theory, critical posthumanism, feminist materialism, and posthuman philosophy. A resource for students and teachers, this comprehensive volume brings together established international scholars and emerging theorists, for timely and astute definitions of a moving target – posthuman humanities and feminist posthumanities. (shrink)

I. Ókor -- II. A középkor és a reneszánsz -- III. Az újkor.

This paper is the sequel of a previous one where we have introduced a paraconsistent logic termed paraclassical logic to deal with 'complementary propositions'. Here, we enlarge upon the discussion by considering certain 'meaning principles', which sanction either some restrictions of 'classical' procedures or the utilization of certain 'classical' incompatible schemes in the domain of the physical theories. Here, the term 'classical' refers to classical physics. Some general comments on the logical basis of a scientific theory are also put in (...) between the text, motivated by the discussion of complementarity. (shrink)