We study the structure of analytic ideals of subsets of the natural numbers. For example, we prove that for an analytic ideal I, either the ideal {X (Ω × Ω: En X ({0, 1,…,n} × Ω } is Rudin-Keisler below I, or I is very simply induced by a lower semicontinuous submeasure. Also, we show that the class of ideals induced in this manner by lsc submeasures coincides with Polishable ideals as well as analytic P-ideals. We study this class of (...) ideals and characterize, for example, when the ideals in it are Fσ or when they carry a locally compact group topology. We apply these results to Borel partial orders to rederive a theorem of Todorcevic and to Borel equivalence relations to answer a question of Kechris and Louveau. As another application we give a characterization of σ-ideals of μ-zero sets for Maharam submeasures μ on the Cantor set which is to a large extent analogous to a characterization of the meager ideal due to Kechris and the author. (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)

We prove that for every family I of closed subsets of a Polish space each Σ 1 1 set can be covered by countably many members of I or else contains a nonempty Π 0 2 set which cannot be covered by countably many members of I. We prove an analogous result for κ-Souslin sets and show that if A ♯ exists for any $A \subset \omega^\omega$ , then the above result is true for Σ 1 2 sets. A theorem (...) of Martin is included stating that this result is also true for weakly homogeneously Souslin sets. As an application of our results we derive from them a general form of Hurewicz's theorem due to Kechris, Louveau, and Woodin and a theorem of Feng on the open covering axiom. Also some well-known theorems on finding "big" closed sets inside of "big" Σ 1 1 and Σ 1 2 sets are consequences of our results. (shrink)

We prove that every analytic set in ω ω × ω ω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set, and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective.

We show that each non-compact Polish group admits a continuous action on a Polish space with non-smooth orbit equivalence relation. We actually construct a free such action. Thus for a Polish group compactness is equivalent to all continuous free actions of this group being smooth. This answers a question of Kechris. We also establish results relating local compactness of the group with its inability to induce orbit equivalence relations not reducible to countable Borel equivalence relations. Generalizing a result of Hjorth, (...) we prove that each non-locally compact, that is, infinite dimensional, separable Banach space has a continuous action on a Polish space with non-Borel orbit equivalence relation, thus showing that this property characterizes non-local compactness among Banach spaces. (shrink)

The "space" of Lascar strong types, on some sort and relative to a given complete theory T, is in general not a compact Hausdorff topological space. We have at least three aims in this paper. The first is to show that spaces of Lascar strong types, as well as other related spaces and objects such as the Lascar group Gal L of T, have well-defined Borel cardinalities. The second is to compute the Borel cardinalities of the known examples as well (...) as of some new examples that we give. The third is to explore notions of definable map, embedding, and isomorphism, between these and related quotient objects. We also make some conjectures, the main one being roughly "smooth if and only if trivial". The possibility of a descriptive set-theoretic account of the complexity of spaces of Lascar strong types was touched on in the paper [E. Casanovas, D. Lascar, A. Pillay and M. Ziegler, Galois groups of first order theories, J. Math. Logic1 305–319], where the first example of a "non-G-compact theory" was given. The motivation for writing this paper is partly the discovery of new examples via definable groups, in [A. Conversano and A. Pillay, Connected components of definable groups and o-minimality I, Adv. Math.231 605–623; Connected components of definable groups and o-minimality II, to appear in Ann. Pure Appl. Logic] and the generalizations in [J. Gismatullin and K. Krupiński, On model-theoretic connected components in some group extensions, preprint, arXiv:1201.5221v1]. (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].

We give strengthened versions of the Herwig–Lascar and Hodkinson–Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous structures. For instance, we establish a coherent form of the extension property for partial automorphisms for certain Fraïssé classes. We deduce from these results that the isometry group of the rational Urysohn space, the automorphism group of the Fraïssé limit of any Fraïssé class that is the class of all ${\cal F}$-free structures, and (...) the automorphism group of any free homogeneous structure over a finite relational language all contain a dense locally finite subgroup. We also show that any free homogeneous structure admits ample generics. (shrink)

We investigate the Tukey order in the class of Fσ ideals of subsets of ω. We show that no nontrivial Fσ ideal is Tukey below a Gδ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, we (...) show that gradually flat ideals are precisely those flat ideals that are Tukey below the ideal of density zero sets. (shrink)

In this paper, we complement proximate or ‘how’ explanations for the origins of language, broadening our perspective to include fitness-consequences explanations, i.e. ultimate, or ‘why’ explanations. We identify the platform of trust as a fundamental prerequisite for the development of a language-like system of symbolic communication. The platform of trust is a social niche in which cheap but honest communication with non-kin is possible, because messages tend to be trusted as a default. We briefly consider the place of the platform (...) of trust on the road map as laid out in the Mirror System Hypothesis. We then turn to recent research on turn-taking in primates, which has been proposed as a precursor of the cooperative structuring of conversation in humans. We suggest, instead, that human turn-taking, in its full richness that makes it an interesting explanatory target, may only appear in a communicative system that is already founded on a community-wide, cooperative platform of trust. (shrink)

The set of design features developed by Charles Hockett in the 1950s and 1960s remains probably the most influential means of juxtaposing animal communication with human language. However, the general theoretical perspective of Hockett is largely incompatible with that of modern language evolution research. Consequently, we argue that his classificatory system—while useful for some descriptive purposes—is of very limited use as a theoretical framework for evolutionary linguistics. We see this incompatibility as related to the ontology of language, i.e. deriving from (...) Hockett’s interest in language as a product rather than a suite of sensorimotor, cognitive and social abilities that enable the use but also acquisition of language by biological creatures. After a reconstruction of Hockett’s views on design features, we raise two criticisms: focus on the means at the expense of content and focus on the code itself rather than the cognitive abilities of its users. Finally, referring to empirical data, we illustrate some of the problems resulting from Hockett’s approach by addressing three specific points—namely arbitrariness and semanticity, cultural transmission, and displacement—and show how the change of perspective allows to overcome those difficulties. (shrink)

There is proposed the analysis of conceptual foundations in researching of Poles’ national character on materials of Julian Leopold Ochorowicz (1850-1917) scientific heritage connected with philosophical and pedagogical implications of his ideas. Ochorowicz’s contribution to interdisciplinary approach on Poles’ national character is emphasizing. The heuristically potential of this approach is explicated using reconstruction and systemizing of his views, which had played a significant role in determining intentionality in discussions on the matter «What philosophy do Poles need?” for the successful self-statement (...) in their national being. Critically evaluating of this experience there is combined with verifying of his theoretical assumptions that should be actual also in Ukrainian social and cultural contexts. Ochorowicz belongs to the group of outstanding Polish scholars with wide scientific interests and original achievements. This article presents his research on history perceived as a collective psychological process. In Poland, Ochorowicz should be regarded as a precursor of psychohistory. An important role in his conception is played by the theory of the so-called residual symptoms, on the basis of which he developed the concept of Poles’ national character with its educational implications. The question about the rudiments of our national character sharpens in border situations, in which those traits, previously presented in a declarative form, are verified. The strength of a nation is encoded in the irreal sphere, i.e. in the sphere of values around which people group themselves. (shrink)

A new approach to semantics, based on ordered Banach spaces, is proposed. The Banach spaces semantics arises as a generalization of the four particular cases: the Giles' approach to belief structures, its generalization to the non-Boolean case, and fuzzy extensions of Boolean as well as of non-Boolean semantics.

The paper describes in detail the procedure of identification of the inner language and an inner logico of a physical theory. The procedure is a generalization of the original ideas of J. von Neuman and G. Birkhoff about quantum logic.

In the 1980s, computer-aided experimental research became standard in the majority of leading research laboratories. Unfortunately, this shift was not adequately reflected in the professional literature related to the philosophy and methodology of science. A new experimentalism did emerge, aimed at adequately describing experimental practice (to be discussed in the first part of this article); however, in its initial phase, it failed to consider the role of computers in experimental research (discussed in the second part). This oversight by the philosophers (...) of science, the proponents of the new experimentalism, is significant and calls for supplementation (addressed in the fourth part). By the turn of the 20 th and 21 st centuries, there were numerous philosophical analyses related to computer experiments, such as computer simulations. However, this article focuses only on classic experiments facilitated by various computer systems (e.g., LHC at CERN). In the final part of this article, I will present examples of aspects of experimental work that have not yet been analyzed and could potentially enhance new experimentalism with insights from computer-aided experiments. (shrink)

Livio Rossetti, Le dialogue socratique, Éditions Les Belles Lettres, Paris 2011, ss. 296.

We construct free algebras in the variety generated by the equivalential algebra with conjunction on dense elements and compute the formula for the free spectrum of this variety. Moreover, we describe the decomposition of free algebras into directly indecomposable factors.

The paper presents an analysis of the ethical, political and economic aspects of human work within two Polish historical periods – the years of the People’s Republic of Poland and after 1989. The starting point for the analysis was the assumption that every time period, each age, leaves a mark on man’s work. Analysis of the People's Republic of Poland period gives an opportunity to consider human work understood as a duty and right of every human guaranteed by the Constitution (...) of 1952. Questioning the principles ruling the labour market by the ideologists of the People’s Republic of Poland and, as a consequence, the politicization of labour, resulted in the collapse of the work ethic. Work, as it was at that time a commonly available good, lost its value, regarded as the source of life satisfaction, and thus became ridiculed. After 1989, in relation to the de-politicization of the Polish labour market, the employee became active in searching for a job. The phenomenon of unemployment resulted in competition on the labour market and the employer was thus given the opportunity to freely select a group of employees. As a result, the employer became a distributor of a ‘rare commodity.’ That, in turn, led to the situation where the approach of employers towards employees turned into the employer's diktat. It is the employer who determines the conditions of employment, standards of work and place of work. A lack of alternative that many employees face often makes them accept the dictated conditions of work. What is more, in Poland we deal with the insufficiently developed participation of employees in managing the enterprises, which is an effect of breaking off the bilateral dependency of employee and employer. (shrink)

We study the variety generated by the three-element equivalential algebra with conjunction on the dense elements. We prove the representation theorem which let us construct the free algebras in this variety.

John Searle’s Chinese Room Argument purports to demonstrate that syntax is not sufficient for semantics, and, hence, because computation cannot yield understanding, the computational theory of mind, which equates the mind to an information processing system based on formal computations, fails. In this paper, we use the CRA, and the debate that emerged from it, to develop a philosophical critique of recent advances in robotics and neuroscience. We describe results from a body of work that contributes to blurring the divide (...) between biological and artificial systems; so-called animats, autonomous robots that are controlled by biological neural tissue and what may be described as remote-controlled rodents, living animals endowed with augmented abilities provided by external controllers. We argue that, even though at first sight, these chimeric systems may seem to escape the CRA, on closer analysis, they do not. We conclude by discussing the role of the body–brain dynamics in the processes that give rise to genuine understanding of the world, in line with recent proposals from enactive cognitive science. (shrink)

Let us consider multimodal logics and. We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and, we construct a connected frame which characterises the fusion. The frame thus obtained has some useful properties. Among others, is countable if both and are countable, and (...) there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point. We also describe a similar construction where we assume the existence of two classes consisting of rooted frames only. Using those classes and frames with so-called -roots, we construct a rooted frame adequate for the fusion of modal logics characterised by the classes under consideration. Both constructions can be used interchangeably. The selection of the construction depends on... (shrink)