We solve two problems from a work of Haskel and Pillay concerning maximal stable quotients of groups ∧-definable in NIP theories. The first result says that if G is a ∧-definable group in a distal theory, then Gst=G00 (where Gst is the smallest ∧-definable subgroup with G∕Gst stable, and G00 is the smallest ∧-definable subgroup of bounded index). In order to get it, we prove that distality is preserved under passing from T to the hyperimaginary expansion Theq. The second result (...) is an example of a group G definable in a nondistal NIP theory for which G=G00, but Gst is not an intersection of definable groups. Our example is a saturated extension of (R,+,[0,1]). Moreover, we make some observations on the question whether there is such an example which is a group of finite exponent. We also take the opportunity and give several characterizations of stability of hyperdefinable sets involving continuous logic. (shrink)

Let [Formula: see text] be a monster model of an arbitrary theory [Formula: see text], let [Formula: see text] be any tuple of bounded length of elements of [Formula: see text], and let [Formula: see text] be an enumeration of all elements of [Formula: see text]. By [Formula: see text] we denote the compact space of all complete types over [Formula: see text] extending [Formula: see text], and [Formula: see text] is defined analogously. Then [Formula: see text] and [Formula: see (...) text] are naturally [Formula: see text]-flows. We show that the Ellis groups of both these flows are of bounded size, providing an explicit bound on this size. Next, we prove that these Ellis groups do not depend on the choice of the monster model [Formula: see text]; thus, we say that these Ellis groups are absolute. We also study minimal left ideals of the Ellis semigroups of the flows [Formula: see text] and [Formula: see text]. We give an example of a NIP theory in which the minimal left ideals are of unbounded size. Then we show that in each of these two cases, boundedness of a minimal left ideal is an absolute property and that whenever such an ideal is bounded, then in some sense its isomorphism type is also absolute. Under the assumption that [Formula: see text] has NIP, we give characterizations of when a minimal left ideal of the Ellis semigroup of [Formula: see text] is bounded. Then we adapt the proof of Theorem 5.7 in Definably amenable NIP groups, J. Amer. Math. Soc. 31 609–641 to show that whenever such an ideal is bounded, a certain natural epimorphism 863–932]) from the Ellis group of the flow [Formula: see text] to the Kim–Pillay Galois group [Formula: see text] is an isomorphism. We also obtain some variants of these results, formulate some questions, and explain differences which occur when the flow [Formula: see text] is replaced by [Formula: see text]. (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 develop a basic theory of rosy groups and we study groups of small Uþ-rank satisfying NIP and having finitely satisfiable generics: Uþ-rank 1 implies that the group is abelian-by-finite, Uþ-rank 2 implies that the group is solvable-by-finite, Uþ-rank 2, and not being nilpotent-by-finite implies the existence of an interpretable algebraically closed field.

We introduce and study model-theoretic connected components of rings as an analogue of model-theoretic connected components of definable groups. We develop their basic theory and use them to describe both the definable and classical Bohr compactifications of rings. We then use model-theoretic connected components to explicitly calculate Bohr compactifications of some classical matrix groups, such as the discrete Heisenberg group ${\mathrm {UT}}_3({\mathbb {Z}})$, the continuous Heisenberg group ${\mathrm {UT}}_3({\mathbb {R}})$, and, more generally, groups of upper unitriangular and invertible upper triangular (...) matrices over unital rings. (shrink)

We generalize the model theory of small profinite structures developed by Newelski to the case of compact metric spaces considered together with compact groups of homeomorphisms and satisfying the existence of m-independent extensions (we call them compact e-structures). We analyze the relationships between smallness and different versions of the assumption of the existence of m-independent extensions and we obtain some topological consequences of these assumptions. Using them, we adopt Newelski's proofs of various results about small profinite structures to compact e-structures. (...) In particular, we notice that a variant of the group configuration theorem holds in this context. A general construction of compact structures is described. Using it, a class of examples of compact e-structures which are not small is constructed. It is also noticed that in an m-stable compact e-structure every orbit is equidominant with a product of m-regular orbits. (shrink)

We present the (Lascar) Galois group of any countable theory as a quotient of a compact Polish group by an F_σ normal subgroup: in general, as a topological group, and under NIP, also in terms of Borel cardinality. This allows us to obtain similar results for arbitrary strong types defined on a single complete type over ∅. As an easy conclusion of our main theorem, we get the main result of [K. Krupiński, A. Pillay and T. Rzepecki, Topological dynamics and (...) the complexity of strong types, Israel J. Math.228 (2018) 863–932] which says that for any strong type defined on a single complete type over ∅, smoothness is equivalent to type-definability. We also explain how similar results are obtained in the case of bounded quotients of type-definable groups. This gives us a generalization of a former result from the paper mentioned above about bounded quotients of type-definable subgroups of definable groups. (shrink)

Let G be a group definable in a monster model $\germ{C}$ of a rosy theory satisfying NIP. Assume that G has hereditarily finitely satisfiable generics and 1 < U þ (G) < ∞. We prove that if G acts definably on a definable set of U þ -rank 1, then, under some general assumption about this action, there is an infinite field interpretable in $\germ{C}$ . We conclude that if G is not solvable-by-finite and it acts faithfully and definably on (...) a definable set of U þ -rank 1, then there is an infinite field interpretable in $\germ{C}$ . As an immediate consequence, we get that if G has a definable subgroup H such that U þ (G) = U þ (H) + 1 and $G/\bigcap _{g\in G}H^{g}$ is not solvable-by-finite, then an infinite field interpretable in $\germ{C}$ also exists. (shrink)

For a NIP theory T, a sufficiently saturated model ${\mathfrak C}$ of T, and an invariant (over some small subset of ${\mathfrak C}$ ) global type p, we prove that there exists a finest relatively type-definable over a small set of parameters from ${\mathfrak C}$ equivalence relation on the set of realizations of p which has stable quotient. This is a counterpart for equivalence relations of the main result of [2] on the existence of maximal stable quotients of type-definable groups (...) in NIP theories. Our proof adapts the ideas of the proof of this result, working with relatively type-definable subsets of the group of automorphisms of the monster model as defined in [3]. (shrink)

We study relationships between certain algebraic properties of groups and rings definable in a first order structure or *-closed in a compact G-space. As a consequence, we obtain a few structural results about ω-categorical rings as well as about small, nm-stable compact G-rings, and we also obtain surprising relationships between some conjectures concerning small profinite groups.

We give a model-theoretic treatment of the fundamental results of Kechris-Pestov-Todorčević theory in the more general context of automorphism groups of not necessarily countable structures. One of the main points is a description of the universal ambit as a certain space of types in an expanded language. Using this, we recover results of Kechris et al. (Funct Anal 15:106–189, 2005), Moore (Fund Math 220:263–280, 2013), Ngyuen Van Thé (Fund Math 222: 19–47, 2013), in the context of automorphism groups of not (...) necessarily countable structures, as well as Zucker (Trans Am Math Soc 368, 6715–6740, 2016). (shrink)

We investigate profinite structures in the sense of Newelski interpretable in fields. We show that profinite structures interpretable in separably closed fields are the same as profinite structures weakly interpretable in . We also find a strong connection with the inverse Galois problem. We give field theoretic constructions of profinite structures weakly interpretable in and satisfying some model theoretic properties, like smallness, m-normality, non-triviality, being -rank 1. For example we interpret in this way the profinite structure consisting of the profinite (...) group together with a distinguished Sylow p-subgroup of its standard structural group. (shrink)

We analyze model-theoretic connected components in extensions of a given group by abelian groups which are defined by means of 2-cocycles with finite image. We characterize, in terms of these 2-cocycles, when the smallest type-definable subgroup of the corresponding extension differs from the smallest invariant subgroup. In some situations, we also describe the quotient of these two connected components. Using our general results about extensions of groups together with Matsumoto–Moore theory or various quasi-characters considered in bounded cohomology, we obtain new (...) classes of examples of groups whose smallest type-definable subgroup of bounded index differs from the smallest invariant subgroup of bounded index. This includes the first known example of a group with this property found by Conversano and Pillay, namely the universal cover of [Formula: see text], as well as various examples of different nature, e.g. some central extensions of free groups or of fundamental groups of closed orientable surfaces. As a corollary, we get that both non-abelian free groups and fundamental groups of closed orientable surfaces of genus [Formula: see text], expanded by predicates for all subsets, have this property, too. We also obtain a variant of the example of Conversano and Pillay for [Formula: see text] instead of [Formula: see text], which was not accessible by the previously known methods. (shrink)

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenPhas unbounded orbit under the action of (...) the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable. (shrink)

We prove that each ω-categorical, generically stable group is solvable-by-finite.

We prove that every ω-categorical, generically stable group is nilpotent-by-finite and that every ω-categorical, generically stable ring is nilpotent-by-finite.

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)

Sixteen years ago, Prahalad and Hart introduced the possibility of both profitably serving the poor and alleviating poverty. This first iteration of the Bottom/Base of the Pyramid approach focused on selling to the poor. In 2008, after ethical criticisms leveled at it, the field moved to BoP 2.0, instead emphasizing business co-venturing. Since 2015, we have witnessed some calls for a new iteration, with the focus broadening to a more sustainable development approach to poverty alleviation. In this paper, we seek (...) to answer the question: How has the BoP approach evolved over the past 16 years, and has it delivered on its early promise? We conducted a systematic review of 276 papers published in journals in this period, utilizing a rigorous correspondence analysis method to map key trends, and then further examined the 22 empirical studies conducted on the BoP approach. Our results suggest that the field has evolved, passing through a number of trends and coming full circle—with our analysis pointing to more recent BoP literature emphasizing similar themes to those espoused in the initial BoP iteration, rather than reflecting the principles espoused in either BoP 2.0 or BoP 3.0. Our analysis also points to a lack of clear evidence that the BoP concept has delivered on its promise either to businesses or to BoP participants. (shrink)

The introspective devices framework proposed by Kammerer and Frankish (this issue) offers an attractive conceptual tool for evaluating and developing accounts of introspection. However, the framework assumes that different views about the nature of introspection can be easily evaluated against a set of common criteria. In this paper, I set out to test this assumption by analysing two formal models of introspection using the introspective device framework. The question I aim to answer is not only whether models developed outside of (...) philosophy can be successfully evaluated against the set of conceptual criteria proposed by Kammerer and Frankish, but also whether this kind of evaluation can reveal some limitations inherent to the framework. (shrink)

Porter and Kramer :78–92, 2006; Harv Bus Rev 89, 62–77, 2011) introduced ‘shared value’ as a ‘new conception of capitalism,’ claiming it is a powerful driver of economic growth and reconciliation between business and society. The idea has generated strong interest in business and academia; however, its theoretical precepts have not been rigorously assessed. In this paper, we provide a systematic and thorough analysis of shared value, focusing on its ontological and epistemological properties. Our review highlights that ‘shared value’ has (...) spread into the language of multiple disciplines, but that its current conceptualization is vague, and it presents important discrepancies in the way it is defined and operationalized, such that it is more of a buzzword than a substantive concept. It also overlaps with many other concepts and lacks empirical grounding. We offer recommendations for defining and measuring the concept, take a step toward disentangling it from related concepts, and identify relevant theories and research methods that would facilitate extending the knowledge frontier on shared value. (shrink)

This article examines the question: How do local organizations deal with competing temporal dynamics when building and implementing base/bottom of the pyramid initiatives? Time has been neglected in the BoP literature to date, yet, addressing poverty in a developing country requires a complex perspective of time. An analysis of 21 semi-structured interviews with locally based organizations implementing BoP initiatives in the Philippines revealed that the organizations had an ambitemporal perspective. In particular, we discover that they harmonize multiple temporal pacers by (...) making strategic decisions about the best mechanism of entrainment to utilize to move their community and any stakeholders to a long-term temporal horizon. We find that organizations manage this process by generating what we term a “third time” via a process of push-and-pull entrainment between the communities, the business, and the different temporal pacers. This article develops a conceptual framework for helping organizations to harmonize competing temporal dynamics to generate a bespoke “third time” for each community they work with. (shrink)

This paper is obituary of Leszek Nowak, one of the greatest Polish philosophers of the XX century.

This chapter contains sections titled: Logical Positivism: Basic Information The Hempelian Model of Explanation in Historiography Popperian Critique of Historicism Conclusion Bibliography.

In this paper, I analyze the shift in Twardowski’s views between his early psychologistic theory of logic and his later anti-psychologistic theory. In particular, I point out that the interpretation suggesting that this change merely involves Twardowski enriching his ontology with products encounters a certain problem in light of his earlier views. To present this problem more precisely, I discuss the foundations of Twardowski’s theory of products, focusing on aspects relevant to the issue of psychologism. Based on this, I reconstruct (...) Twardowski’s theory of logic and highlight where he identified the fallacy of psychologism. I contrast this reconstructed theory with Twardowski’s earlier views at key points and demonstrate that the difference between his early psychologistic theory and his later anti-psychologistic theory is a matter of a shift in emphasis rather than a significant change in the theoretical system itself, and that Twardowski himself understood it as such. (shrink)

Weakly acyclic games form a natural generalization of the class of games that have the finite improvement property. In such games one stipulates that from any initial joint strategy some finite improvement path exists. We classify weakly acyclic games using the concept of a scheduler introduced in Simon and Apt. We also show that finite games that can be solved by the iterated elimination of never best response strategies are weakly acyclic. Finally, we explain how the schedulers allow us to (...) improve the bounds on finding a Nash equilibrium in a weakly acyclic game. (shrink)

The proposal that probabilistic inference and unconscious hypothesis testing are central to information processing in the brain has been steadily gaining ground in cognitive neuroscience and associated fields. One popular version of this proposal is the new theoretical framework of predictive processing or prediction error minimization, which couples unconscious hypothesis testing with the idea of ‘active inference’ and claims to offer a unified account of perception and action. Here we will consider one outstanding issue that still looms large at the (...) core of the PEM framework: the lack of a clear criterion for distinguishing conscious states from unconscious ones. In order to fulfill the promise of becoming a unifying framework for describing and modeling cognition, PEM needs to be able to differentiate between conscious and unconscious mental states or processes. We will argue that one currently popular view, that the contents of conscious experience are determined by the ‘winning hypothesis’, falls short of fully accounting for conscious experience. It ignores the possibility that some states of a system can control that system’s behavior even though they are apparently not conscious. What follows from this is that the ‘winning hypothesis’ view does not provide a complete account of the difference between conscious and unconscious states in the probabilistic brain. We show how this problem for the received view can be resolved by augmenting PEM with Daniel Dennett’s multiple drafts model of consciousness. This move is warranted by the similar roles that attention and internal competition play in both the PEM framework and the multiple drafts model. (shrink)

Zakład Kulturoznawstwa Wydział Pedagogiki i Psychologii Uniwersytet w Białymstoku.

In the present paper an interpretation of the political dimension of pragmatic aesthetic reflection is proposed. The interconnection between politics and aesthetics in three classic American pragmatists: William James (1842–1910), John Dewey (1859–1952), and George Herbert Mead (1863–1931) is evoked. The author claims that by emphasizing the role of democratic values in philosophy and life, the classic American pragmatists encroach upon the field of the arts and aesthetics. Their emphasis put upon individual activity, free expression of thoughts, plurality of the (...) forms of expression, and acceptance of criticism as a tool helping create better solutions in human cooperation can easily be converted into the postulates about the character of the artistic principles and of the nature of the aesthetic norms and values. (shrink)

In the present paper, the author looks at the political dimension of some trends in the visual arts within twentieth-century avant-garde groups (cubism, expressionism, fauvism, Dada, abstractionism, surrealism) through George Santayana’s idea of vital liberty. Santayana accused the avant-gardists of social and political escapism, and of becoming unintentionally involved in secondary issues. In his view, the emphasis they placed on the medium (or diverse media) and on treating it as an aim in itself, not, as it should be, as a (...) transmitter through which a stimulating relationship with the environment can be had, was accompanied by a focus on fragments of life and on parts of existence, and, on the other hand, by a de facto rejection of ontology and cosmology as being crucial to understanding life and the place of human beings in the universe. The avant-gardists became involved in political life by responding excessively to the events of the time, instead of to the everlasting problems that are the human lot. (shrink)

Pomiędzy filozofią a resztą kultury rośnie przepaść. Podczas gdy filozofowie są całkowicie przekonani o ważności swojej dziedziny i doniosłości tego, co się w niej robi – jej pytań, jej argumentacji, jej odpowiedzi, jej wynalazków pojęciowych, jej błyskotliwych idei, to niefilozofowie coraz powszechniej ważność tę kwestionują, w doniosłość powątpiewają, argumentacji nie cenią, błyskotliwości nie dostrzegają i w ogóle nie pojmują o co cały ambaras. Wszak filozofia drwa nie narąbie, wirusów z komputera nie usunie, cen w sklepach nie obniży, w rubryce „patenty (...) i wdrożenia” napisze „brak”. Zapytajmy więc: po co naszej kulturze filozofowanie? Nie filozofowie i nie instytuty filozoficznych badań i kształcenia filozoficznego, ale właśnie – filozofowanie. Żeby odpowiedzieć na takie pytanie, potrzeba nie tylko filozofii, ale także dobrych narzędzi z innych dziedzin nauki. Trzeba zapytać, jakiego rodzaju grą kulturową jest filozofowanie? Ilu z nas w nią gra? I co się wtedy dzieje? Czy filozofujemy na co dzień, czy tylko od święta? Niniejsza książka ani nie popularyzuje, ani nie przybliża tego, co robią filozofowie. Zamiast tego prowadzi Czytelników od rozmów w pociągach do teorii czerpanych z filozofii i socjologii wiedzy, od lektury nagłówków prasowych do teorii kultury, od obrazów epidemii i biografii Spinozy do studiów nad nauką. Stara się przy tym na pytania wyżej postawione jak najogólniej odpowiedzieć, a przepaść zasypać, pokazać przy tym, że filozofia od swego kulturowego otoczenia nie jest i nigdy nie była odizolowana. Przeciwnie, filozofowanie tak bardzo i w tak licznych miejscach w tkankę kultury wrosło, że bez niego tkanka ta porozrywałaby się na strzępy, że dla kultury współczesnej filozofowanie w najrozmaitszych przejawach jest czymś koniecznym, jest warunkiem trwania, życia i rozwoju. (shrink)

In the paper we introduce two conditions and ) which are strengthenings of Birkhoff’s conditions. We prove that an upper continuous and strongly atomic lattice is distributive if and only if it satisfies and ). This result extends a theorem of R.P. Dilworth characterizing distributivity in terms of local distributivity and a theorem of M. Ward characterizing distributivity by means of covering diamonds.

Canaanite Scribes in the Amarna Letters. By Juan-Pablo Vita. Alter Orient und Altes Testament, vol. 406. Münster: Ugarit-Verlag, 2015. Pp. xii + 179, 78 plates. €97.