We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, (...) and homocyclic groups. Connections are made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted. (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)

The definition of a pseudofinite structure can be translated verbatim into continuous logic, but it also gives rise to a stronger notion and to two parallel concepts of pseudocompactness. Our purpose is to investigate the relationship between these four concepts and establish or refute each of them for several basic theories in continuous logic. Pseudofiniteness and pseudocompactness turn out to be equivalent for relational languages with constant symbols, and the four notions coincide with the standard pseudofiniteness in the case (...) of classical structures, but the details appear to be slightly more important here than in the usual translation of definitions from classical logic. We also prove that injective “formula-definable” endofunctions are surjective, and conversely, in strongly pseudofinite omega-saturated structures. (shrink)

In this article we explore some properties of H-structures which are introduced in [2]. We describe a construction of H-structures based on one-dimensional asymptotic classes which preserves pseudofiniteness. That is, the H-structures we construct are ultraproducts of finite structures. We also prove that under the assumption that the base theory is supersimple of SU-rank one, there are no new definable groups in H-structures. This improves the corresponding result in [2].

In a relational language consisting of a single relation R, we investigate pseudofiniteness of certain Hrushovski constructions obtained via predimension functions. It is notable that the arity of the relation R plays a crucial role in this context. When R is ternary, by extending the methods recently developed by Brody and Laskowski, we interpret 〈Q+,<〉 in the 〈K+,≤∗〉-generic and prove that this structure is not pseudofinite. This provides a negative answer to the question posed in an earlier work by (...) Evans and Wong. This result, in fact, unfolds another aspect of complexity of this structure, along with undecidability and the strict order property proved in the mentioned earlier works. On the other hand, when R is binary, it can be shown that the 〈K+,≤∗〉-generic is decidable and pseudofinite. (shrink)

We develop “local NIP group theory” in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure G expanding a group, and left invariant NIP formula δ...

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory.

We continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$ (...) of countable models of the theory of a fixed Baldwin–Shi hypergraph with $\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $ if and only if the dimension of $\mathfrak{M}_\beta $ is at most the dimension of $\mathfrak{M}_\gamma $ and that each countable model is isomorphic to some $\mathfrak{M}_\beta $. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω-stable theory with a nonlocally modular regular type, answering a question of Pillay in [11]. (shrink)

This article addresses the question which structures occur as fixed structures of stable structures with a generic automorphism. In particular we give a Galois theoretic characterization. Furthermore, we prove that any pseudofinite field is the fixed field of some model ofACFA, any one-free pseudo-differentially closed field of characteristic zero is the fixed field of some model ofDCFA, and that any one-free PAC field of finite degree of imperfection is the fixed field of some model ofSCFA.

Abstract3′ untranslated regions (3′ UTRs) of mRNAs have many functions, including mRNA processing and transport, translational regulation, and mRNA degradation and stability. These different functions require cis‐elements in 3′ UTRs that can be either sequence motifs or RNA structures. Here we review the role of secondary structures in the functioning of 3′ UTRs and discuss some of the trans‐acting factors that interact with these secondary structures in eukaryotic organisms. We propose potential participation of 3′‐UTR secondary structures (...) in cytoplasmic polyadenylation in the model organism Drosophila melanogaster. Because the secondary structures of 3′ UTRs are essential for post‐transcriptional regulation of gene expression, their disruption leads to a wide range of disorders, including cancer and cardiovascular diseases. Trans‐acting factors, such as STAU1 and nucleolin, which interact with 3′‐UTR secondary structures of target transcripts, influence the pathogenesis of neurodegenerative diseases and tumor metastasis, suggesting that they are possible therapeutic targets. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

While contemporary philosophers have devoted vast amounts of attention to the language we use in describing and finding our way about the world of everyday experience, they have, with few exceptions, refused to see this world itself as a fitting object of theoretical concern. In what follows I shall seek to show how the commonsensical world might be treated ontologically as an object of investigation in its own right. At the same time I shall seek to establish how such a (...) treatment might help us better philosophically to understand the structures of both physical reality and cognition. (shrink)

While mechanistic explanation and, to a lesser extent, nomological explanation are well-explored topics in the philosophy of biology, topological explanation is not. Nor is the role of diagrams in topological explanations. These explanations do not appeal to the operation of mechanisms or laws, and extant accounts of the role of diagrams in biological science explain neither why scientists might prefer diagrammatic representations of topological information to sentential equivalents nor how such representations might facilitate important processes of explanatory reasoning unavailable to (...) scientists who restrict themselves to sentential representations. Accordingly, relying upon a case study about immune system vulnerability to attacks on CD4+ T-cells, I argue that diagrams group together information in a way that avoids repetition in representing topological structure, facilitate identification of specific topological properties of those structures, and make available to controlled processing explanatorily salient counterfactual information about topological structures, all in ways that sentential counterparts of diagrams do not. (shrink)

This paper presents a theory of situated part structures involving the notion of an integrated and not just a part-of relation. The theory is applied in particular to the semantics of the modifiers 'whole' and 'individual', as in 'the whole collection' and 'the individual students'. The adnominal modifiers 'whole' and 'individual' have been entirely been ignored in the linguistic and philosophical literature, even though they pose significant challenges for standard views of reference, of the semantics of referential NPs, and (...) for ontology (the exception being medieval philosophy of language where 'whole' has received significant attention). 'Whole' strikingly displays two opposite readings: 'The whole collection is expensive' can mean - 'as a whole' or 'every part'. The paper proposes that the two readings be traced to two different conceptions of part structures of objects: one according to which the parts of an objects are just the material parts and another, Aristotelian conception according to which the parts of an object include properties of form. (shrink)

This is a collection of published and unpublished essays by distinguished philosopher Michael E. Bratman of Stanford University. They revolve around his influential theory, know as the "planning theory of intention and agency." Bratman's primary concern is with what he calls "strong" forms of human agency--including forms of human agency that are the target of our talk about self-determination, self-government, and autonomy. These essays are unified and cohesive in theme, and will be of interest to philosophers in ethics and metaphysics.

What is the one big idea of Koselleck’s Historik understood as a methodological framework for the attempt to combine a theory of historical times with a theory of historical time? In part (1) of this paper, I criticize the two most basic attempts to understand Koselleck’s one big idea as mistaken because they are exclusively interested either in history (in the singular) or in histories (in the plural) and thus miss the central relevance of structures of repetition (“Wiederholungsstrukturen”) for (...) Koselleck’s Historik. In part (2), I will clarify the rather hidden pre-history, the main ambition, the theoretical context and the substantial content of Koselleck’s concept of structures of repetition in history and language. In part (3), I will discuss four historiographical consequences of Koselleck’s structures of repetition. I will end the paper by observing a remarkable theoretical affinity between Barrington Moore’s search for recurring patterns in the field of sociology and Koselleck’s structures of repetition in history and language. Moore’s work illustrates the historiographical potential of the one big idea of Koselleck’s Historik better than any other work I am aware of. (shrink)

The semantic approach to scientific representation is now long established as a favourite amongst philosophers of science. One of the foremost strains of this approach—the model-theoretic approach —is to represent scientific theories as families of models, all of which satisfy or ‘make true’ a given set of constraints. However some authors have criticised the approach on the grounds that certain scientific theories are logically inconsistent, and there can be no models of an inconsistent set of constraints. Thus it would seem (...) that the MTA fails to represent inconsistent scientific theories at all, and this raises concerns about the way it represents in general. In a series of papers and a recent book da Costa and French have developed a variant of the MTA approach which they call ‘partial structures’, and which they claim can accommodate inconsistent theories. I assess this claim, looking to two theories which have been called ‘inconsistent’: Bohr’s theory of the atom and classical electrodynamics. (shrink)

Powers often depend on structures. It is because of the eye’s structure that it confers the power of sight; destroy that structure, and you destroy the power. I sketch an antireductive yet broadly naturalistic account of the relation between powers and structures. Powers, it says, are embodied in structures. When applied to philosophy of mind, this view resembles classic emergentist theories. I nevertheless argue that it differs from them in crucial respects that insulate it from the problems (...) that beset them – including the problem of emergence and the problem of mental causation. (shrink)

This paper first investigates logical characterizations of different structures of opposition that extend the square of opposition in a way or in another. Blanché’s hexagon of opposition is based on three disjoint sets. There are at least two meaningful cubes of opposition, proposed respectively by two of the authors and by Moretti, and pioneered by philosophers such as J. N. Keynes, W. E. Johnson, for the former, and H. Reichenbach for the latter. These cubes exhibit four and six squares (...) of opposition respectively. We clarify the differences between these two cubes, and discuss their gradual extensions, as well as the one of the hexagon when vertices are no longer two-valued. The second part of the paper is dedicated to the use of these structures of opposition for discussing the comparison of two items. Comparing two items usually involves a set of relevant attributes whose values are compared, and may be expressed in terms of different modalities such as identity, similarity, difference, opposition, analogy. Recently, J.-Y. Béziau has proposed an “analogical hexagon” that organizes the relations linking these modalities. Elementary comparisons may be a matter of degree, attributes may not have the same importance. The paper studies in which ways the structure of the hexagon may be preserved in such gradual extensions. As another illustration of the graded hexagon, we start with the hexagon of equality and inequality due to R. Blanché and extend it with fuzzy equality and fuzzy inequality. Besides, the cube induced by a tetra-partition can account for the comparison of two items in terms of preference, reversed preference, indifference and non-comparability even if these notions are a matter of degree. The other cube, which organizes the relations between the different weighted qualitative aggregation modes, is more relevant for the attribute-based comparison of items in terms of similarity. (shrink)

Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to the non-commutative setting. We study their structure, establish a representation theorem for them in terms of twist structures and conuclei that results in a categorical adjunction, and explore situations where the representation is actually an isomorphism. In the latter case, the adjunction is elevated to a categorical equivalence. (...) By applying this representation to the original motivating special cases we bring to the surface their underlying similarities. (shrink)

The ability to process center‐embedded structures has been claimed to represent a core function of the language faculty. Recently, several studies have investigated the learning of center‐embedded dependencies in artificial grammar settings. Yet some of the results seem to question the learnability of these structures in artificial grammar tasks. Here, we tested under which exposure conditions learning of center‐embedded structures in an artificial grammar is possible. We used naturally spoken syllable sequences and varied the presence of prosodic (...) cues. The results suggest that mere distributional information does not suffice for successful learning. Prosodic cues marking the boundaries of the major relevant units, however, can lead to learning success. Thus, our data are consistent with the hypothesis that center‐embedded syntactic structures can be learned in artificial grammar tasks if language‐like acoustic cues are provided. (shrink)

In The Structures of History Christopher Lloyd questions whether narration on its own can provide a real understanding of history, and addresses in philosophical and practical terms the fundamental problems of whether it is possible to know and to explain the history of human societies, and if so how these tasks might be approached. The book revolves around an inquiry into the general nature of historical structures, how these have been studied by historians, anthropologists, sociologists and philosophers, and (...) how they relate to events, actions and beliefs. The author draws upon a wide range of reference in the philosophy of history and science, and in the writings of historians and social scientists during the last two centuries. The thrust of his account is against the relativism of such as Rorty, Foucault and Derrida, and for the complex socio-historical realism exemplified in the writings of Geertz, Gellner, Ladurie and Mann. Christopher Lloyd concludes that an objective understanding of the past is not an impossible ambition, and he provides a searching analysis of the framework and methods necessary to its realization. (shrink)

This paper describes a method for analyzing a corpus of descriptions collected through micro-phenomenological interviews. This analysis aims at identifying the structure of the singular experiences which have been described, and in particular their diachronic structure, while unfolding generic experiential structures through an iterative approach. After summarizing the principles of the micro-phenomenological interview, and then describing the process of preparation of the verbatim, the article presents on the one hand, the principles and conceptual devices of the analysis method and (...) on the other hand several dimensions of the analysis process: the modes of structural unfolding of generic structures, the mutual guidance of the processes of structural and experiential unfolding, the tracking of analysis processes, and finally the assessment of analysis results. (shrink)

The partial structures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model‐theoretic techniques in the philosophy of (...) science. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed. (shrink)

This chapter contains sections titled: Introduction The Once Received View (ORV) Criticisms of the ORV The “Model Model” of Scientific Theories Mechanisms: Investigating Nonformal Patterns in Scientific Theories Conclusion.

The partial structures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model-theoretic techniques in the philosophy of (...) science. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed. (shrink)

This paper discusses how facet-like structures occur as a commonplace feature in a variety of computer science disciplines as a means for structuring class hierarchies. The paper then focuses on a mathematical model for facets (and class hierarchies in general), called formal concept analysis, and discusses graphical representations of faceted systems based on this model.

In recent years Community Supported Agriculture (CSA), an innovative grassroots movement connecting consumers with a local farm, has rapidly spread across Germany and other industrialized countries. An increasing number of consumers who are dissatisfied with conventional food supply chains have signed up to receive fresh produce, support a local community and protect the environment. So far little is known, though, about the underlying value structures of CSA. Nevertheless, identifying factors influencing consumers’ interest in CSA is regarded as a major (...) aim of contemporary CSA research. This research aims to provide insights into CSA members’ value structures, and delineates CSA members by comparing their value structures to those of the German population in general. Schwartz’s Portrait Value Questionnaire was used in a standardized online survey of CSA members to mirror the dataset which is available to the German public via the European Social Survey. A total sample of 205 CSA members was used to examine common value structures by comparing them with the German public. This study’s findings strongly indicate that a CSA membership goes along with a characteristic value pattern: CSA members highly appreciate self-transcendence and openness to change, but tend to reject conservation and self-enhancement values. Addressing members’ preference for openness to change and self-transcendence may help CSAs to reduce fluctuation rates. It might also enhance CSA marketing strategy by addressing potential members’ interests more precisely. Therefore, identifying and communicating common values of a CSA might be a key factor in determining its long-term success and stability. (shrink)

How do humans, their needs, and technology interact in society? Marcel Siegler explores the dialectical relationship between human needs and desires, the demands and requirements of the built world, and the forms of organization that hold both humans and the built world together. He argues that complex societal constellations emerge from the actions individuals perform with the technological means at hand to satisfy their needs and desires in the short and long run. Based on a novel, complementary reading of French (...) philosopher Jean-Paul Sartre, the study develops a conceptual framework for analyzing the intricate machinations of sociotechnical systems from a perspective on situated human-technology interaction. (shrink)

Hrushovski originated the study of “flat” stable structures in constructing a new strongly minimal set and a stable 0-categorical pseudoplane. We exhibit a set of axioms which for collections of finite structure with dimension function δ give rise to stable generic models. In addition to the Hrushovski examples, this formalization includes Baldwin's almost strongly minimal non-Desarguesian projective plane and several others. We develop the new case where finite sets may have infinite closures with respect to the dimension function δ. (...) In particular, the generic structure need not be ω-saturated and so the argument for stability is significantly more complicated. We further show that these structures are “flat” and do not interpret a group. (shrink)

We show: for every noncomputable c.e. incomplete c-degree, there exists a nonspeedable c-degree incomparable with it; The c-degree of a hypersimple set includes an infinite collection of \-degrees linearly ordered under \ with order type of the integers and consisting entirely of hypersimple sets; there exist two c.e. sets having no c.e. least upper bound in the \-reducibility ordering; the c.e. \-degrees are not dense.