Results for 'permutation groups'

998 found
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  1. Supplements of Bounded Permutation Groups.Stephen Bigelow - 1998 - Journal of Symbolic Logic 63 (1):89-102.
    Let λ ≤ κ be infinite cardinals and let Ω be a set of cardinality κ. The bounded permutation group B λ (Ω), or simply B λ , is the group consisting of all permutations of Ω which move fewer than λ points in Ω. We say that a permutation group G acting on Ω is a supplement of B λ if B λ G is the full symmetric group on Ω. In [7], Macpherson and Neumann claimed to (...)
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  2.  18
    Binary Relations and Permutation Groups.Hajnal Andréka & Ivo Düntsch - 1995 - Mathematical Logic Quarterly 41 (2):197-216.
    We discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed and essentially unique. Thus, we obtain the surprising result that on such sets, logic with three variables is as powerful in expression as full first order (...)
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  3.  11
    Cardinal Invariants Related to Permutation Groups.Bart Kastermans & Yi Zhang - 2006 - Annals of Pure and Applied Logic 143 (1):139-146.
    We consider the possible cardinalities of the following three cardinal invariants which are related to the permutation group on the set of natural numbers: the least cardinal number of maximal cofinitary permutation groups; the least cardinal number of maximal almost disjoint permutation families; the cofinality of the permutation group on the set of natural numbers.We show that it is consistent with that ; in fact we show that in the Miller model.
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  4.  16
    Predicate-Induced Permutation Groups.M. Gerner - 2012 - Journal of Semantics 29 (1):109-144.
    Natural languages abound in combinatorial phenomena that are related to the predicate of the sentence and its ability to permute noun phrase arguments. After compiling several illustrative phenomena of natural languages, I propose a novel analysis in terms of permutation groups, a concept borrowed from mathematical combinatorics that is ubiquitous in applied sciences. I show that each natural language predicate of degree n (n natural number) can be associated with two permutation groups of degree n. The (...)
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  5.  25
    Homogeneity of Infinite Permutation Groups.Saharon Shelah & Simon Thomas - 1989 - Archive for Mathematical Logic 28 (2):143-147.
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  6.  10
    On Linearly Ordered Sets and Permutation Groups of Countable Degree.Hans Läuchli & Peter M. Neumann - 1988 - Archive for Mathematical Logic 27 (2):189-192.
  7.  21
    Normal Subgroups of Nonstandard Symmetric and Alternating Groups.John Allsup & Richard Kaye - 2007 - Archive for Mathematical Logic 46 (2):107-121.
    Let ${\mathfrak{M}}$ be a nonstandard model of Peano Arithmetic with domain M and let ${n \in M}$ be nonstandard. We study the symmetric and alternating groups S n and A n of permutations of the set ${\{0,1,\ldots,n-1\}}$ internal to ${\mathfrak{M}}$ , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide evidence that A n and S n are not split extensions by these normal subgroups, by showing that any such complement (...)
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  8.  24
    Exclusion Principles as Restricted Permutation Symmetries.S. Tarzi - 2003 - Foundations of Physics 33 (6):955-979.
    We give a derivation of exclusion principles for the elementary particles of the standard model, using simple mathematical principles arising from a set theory of identical particles. We apply the theory of permutation group actions, stating some theorems which are proven elsewhere, and interpreting the results as a heuristic derivation of Pauli's Exclusion Principle (PEP) which dictates the formation of elements in the periodic table and the stability of matter, and also a derivation of quark confinement. We arrive at (...)
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  9.  10
    Failure of N‐Uniqueness: A Family of Examples.Elisabetta Pastori & Pablo Spiga - 2011 - Mathematical Logic Quarterly 57 (2):133-148.
    In this paper, the connections between model theory and the theory of infinite permutation groups are used to study the n-existence and the n-uniqueness for n-amalgamation problems of stable theories. We show that, for any n ⩾ 2, there exists a stable theory having -existence and k-uniqueness, for every k ⩽ n, but has neither -existence nor -uniqueness. In particular, this generalizes the example, for n = 2, due to Hrushovski given in 3. © 2011 WILEY-VCH Verlag GmbH (...)
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  10.  8
    Reconstructible and Half-Reconstructible Tournaments: Application to Their Groups of Hemimorphisms.Youssef Boudabbous - 1999 - Mathematical Logic Quarterly 45 (3):421-431.
    Let T and T1 be tournaments with n elements, E a basis for T, E′ a basis for T′, and k ≥ 3 an integer. The dual of T is the tournament T” of basis E defined by T = T for all x, y ε E. A hemimorphism from T onto T′ is an isomorphism from T onto T” or onto T. A k-hemimorphism from T onto T′ is a bijection f from E to E′ such that for any (...)
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  11.  26
    Russell's Alternative to the Axiom of Choice.Norbert Brunner & Paul Howard - 1992 - Mathematical Logic Quarterly 38 (1):529-534.
    We prove the independence of some weakenings of the axiom of choice related to the question if the unions of wellorderable families of wellordered sets are wellorderable.
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  12.  22
    Invariance and Definability, with and Without Equality.Denis Bonnay & Fredrik Engström - 2018 - Notre Dame Journal of Formal Logic 59 (1):109-133.
    The dual character of invariance under transformations and definability by some operations has been used in classical works by, for example, Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves could be characterized in terms of invariance. In this article, we generalize a correspondence due to Krasner between invariance under groups of permutations and definability in L∞∞ so as to cover the cases that are of interest in the logicality debates, getting McGee’s theorem about (...)
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  13.  13
    Polynomial-Time Abelian Groups.Douglas Cenzer & Jeffrey Remmel - 1992 - Annals of Pure and Applied Logic 56 (1-3):313-363.
    This paper is a continuation of the authors' work , where the main problem considered was whether a given recursive structure is recursively isomorphic to a polynomial-time structure. In that paper, a recursive Abelian group was constructed which is not recursively isomorphic to any polynomial-time Abelian group. We now show that if every element of a recursive Abelian group has finite order, then the group is recursively isomorphic to a polynomial-time group. Furthermore, if the orders are bounded, then the group (...)
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  14.  92
    Diagrams and Proofs in Analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.
    This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role (...)
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  15.  11
    Reducts of Random Hypergraphs.Simon Thomas - 1996 - Annals of Pure and Applied Logic 80 (2):165-193.
    For each k 1, let Γk be the countable universal homogeneous k-hypergraph. In this paper, we shall classify the closed permutation groups G such that Aut G Sym. In particular, we shall show that there exist only finitely many such groups G for each k 1. We shall also show that each of the associated reducts of Γk is homogeneous with respect to a finite relational language.
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  16.  14
    Finite Covers with Finite Kernels.David M. Evans - 1997 - Annals of Pure and Applied Logic 88 (2-3):109-147.
    We are concerned with the following problem. Suppose Γ and Σ are closed permutation groups on infinite sets C and W and ρ: Γ → Σ is a non-split, continuous epimorphism with finite kernel. Describe the possibilities for ρ. Here, we consider the case where ρ arises from a finite cover π: C → W. We give reasonably general conditions on the permutation structure W;Σ which allow us to prove that these covers arise in two possible ways. (...)
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  17.  28
    ℵ0-Categorical Tree-Decomposable Structures.A. H. Lachlan - 1992 - Journal of Symbolic Logic 57 (2):501 - 514.
    Our purpose in this note is to study countable ℵ0-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.
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  18.  6
    $Aleph_0$-Categorical Tree-Decomposable Structures.A. H. Lachlan - 1992 - Journal of Symbolic Logic 57 (2):501-514.
    Our purpose in this note is to study countable $\aleph_0$-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.
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  19. Epistemically Pernicious Groups and the Groupstrapping Problem.Kenneth Boyd - 2018 - Social Epistemology 33 (1):61-73.
    Recently, there has been growing concern that increased partisanship in news sources, as well as new ways in which people acquire information, has led to a proliferation of epistemic bubbles and echo chambers: in the former, one tends to acquire information from a limited range of sources, ones that generally support the kinds of beliefs that one already has, while the latter function in the same way, but possess the additional characteristic that certain beliefs are actively reinforced. Here I argue, (...)
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  20. Social Structures and the Ontology of Social Groups.Katherine Ritchie - forthcoming - Philosophy and Phenomenological Research.
    Social groups—like teams, committees, gender groups, and racial groups—play a central role in our lives and in philosophical inquiry. Here I develop and motivate a structuralist ontology of social groups centered on social structures (i.e., networks of relations that are constitutively dependent on social factors). The view delivers a picture that encompasses a diverse range of social groups, while maintaining important metaphysical and normative distinctions between groups of different kinds. It also meets the constraint (...)
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  21. Replacing Race: Interactive Constructionism About Racialized Groups.Adam Hochman - 2017 - Ergo: An Open Access Journal of Philosophy 4:61-92.
    In this paper I defend anti-realism about race and a new theory of racialization. I argue that there are no races, only racialized groups. Many social constructionists about race have adopted racial formation theory to explain how ‘races’ are formed. However, anti-realists about race cannot adopt racial formation theory, because it assumes the reality of race. I introduce interactive constructionism about racialized groups as a theory of racialization for anti-realists about race. Interactive constructionism moves the discussion away from (...)
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  22. What Are Social Groups? Their Metaphysics and How to Classify Them.Brian Epstein - forthcoming - Synthese:1-34.
    This paper presents a systematic approach for analyzing and explaining the nature of social groups. I argue against prominent views that attempt to unify all social groups or to divide them into simple typologies. Instead I argue that social groups are enormously diverse, but show how we can investigate their natures nonetheless. I analyze social groups from a bottom-up perspective, constructing profiles of the metaphysical features of groups of specific kinds. We can characterize any given (...)
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  23.  36
    Corporate Governance and Corruption: Ethical Dilemmas of Asian Business Groups[REVIEW]Marie Rama - 2012 - Journal of Business Ethics 109 (4):501-519.
    This study looks at how the corporate governance of family-owned business groups, the most dominant form of private sector organising in Asia, deals with different forms of corruption during the course of common business transactions. As a part of an ethnographic study conducted in 2007 to look at the impact of corporate governance reforms in the Philippines, one of the emergent themes from the study was the presence of significant corruption in the business environment of the country. A total (...)
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  24. P-Compatible Abelian Groups.Krystyna Mruczek-Nasieniewska - 2005 - Logic and Logical Philosophy 14 (2):253-263.
    Let τ : F → N be a type of a variety V . Every partition Pof the set F determines a so-called P-compatible variety. We consider thevarieties GnP defined by so-called P-compatible identities of Abelian groupswith exponent n. Besides, we study a connection between the lattice of allpartitions of the set F and the lattice of all subvarieties of the variety definedby some kind of P-compatible identities — externally compatible identitiessatisfied in the class of all Abelian groups with (...)
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  25.  19
    On a Definition of a Variety of Monadic ℓ-Groups.José Luis Castiglioni, Renato A. Lewin & Marta Sagastume - 2014 - Studia Logica 102 (1):67-92.
    In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor ${{\mathsf{K}^\bullet}}$ , motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case (...)
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  26.  28
    Sustainability and New Models of Consumption: The Solidarity Purchasing Groups in Sicily. [REVIEW]Luigi Cembalo, Giuseppina Migliore & Giorgio Schifani - 2013 - Journal of Agricultural and Environmental Ethics 26 (1):281-303.
    European society, with its steadily increasing welfare levels, is not only concerned with food (safety, prices), but also with other aspects such as biodiversity loss, landscape degradation, and pollution of water, soil, and atmosphere. To a great extent these concerns can be translated into a larger concept named sustainable development, which can be defined as a normative concept by). Sustainability in the food chain means creating a new sustainable agro-food system while taking the institutional element into account. While different concepts (...)
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  27.  13
    Placing Collaborative Circles in Strategic Action Fields: Explaining Differences Between Highly Creative Groups.John N. Parker & Ugo Corte - 2017 - Sociological Theory 35 (4):261-287.
    Collaborative circles theory explains how innovative small groups develop and win acceptance of their creative work but assumes a single type of circle and would benefit from considering how circles are affected by the strategic action fields in which they operate. We do so by synthesizing research on art, science, philosophy, and social movements to identify five field characteristics that influence circles and their creative potentials (i.e., attention space, consensus, social control, resources, and organizational and geographical contexts). We then (...)
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  28.  40
    On the Equivalence Between MV-Algebras and L-Groups with Strong Unit.Eduardo J. Dubuc & Y. A. Poveda - 2015 - Studia Logica 103 (4):807-814.
    In “A new proof of the completeness of the Lukasiewicz axioms” Chang proved that any totally ordered MV-algebra A was isomorphic to the segment \}\) of a totally ordered l-group with strong unit A *. This was done by the simple intuitive idea of putting denumerable copies of A on top of each other. Moreover, he also show that any such group G can be recovered from its segment since \^*}\), establishing an equivalence of categories. In “Interpretation of AF C (...)
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  29.  37
    Ethics in the Humanities: Findings From Focus Groups[REVIEW]Cheryl K. Stenmark, Alison L. Antes, Laura E. Martin, Zhanna Bagdasarov, James F. Johnson, Lynn D. Devenport & Michael D. Mumford - 2010 - Journal of Academic Ethics 8 (4):285-300.
    This project examined the ethical issues faced by academics and professionals in the Humanities. We conducted focus groups to gather information about the ethical concerns in these fields and used the qualitative data arising from the discussions to create a taxonomy that represents the structure of ethical issues in the Humanities. A key implication of our findings is that while the focus of ethics research and interventions has been primarily on the sciences and engineering, academics and professionals in other (...)
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  30.  46
    Symmetry, Structure, and the Constitution of Objects.Steven French - 2001 - PhilSci Archive.
    In this paper I focus on the impact on structuralism of the quantum treatment of objects in terms of symmetry groups and, in particular, on the question as to how we might eliminate, or better, reconceptualise such objects in structural terms. With regard to the former, both Cassirer and Eddington not only explicitly and famously tied their structuralism to the development of group theory but also drew on the quantum treatment in order to further their structuralist aims and here (...)
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  31.  34
    Finitely Generated Free MV-Algebras and Their Automorphism Groups.Antonio Di Nola, Revaz Grigolia & Giovanni Panti - 1998 - Studia Logica 61 (1):65-78.
    The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...)
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  32.  52
    Failure and Uses of Jaynes’ Principle of Transformation Groups.Alon Drory - 2015 - Foundations of Physics 45 (4):439-460.
    Bertand’s paradox is a fundamental problem in probability that casts doubt on the applicability of the indifference principle by showing that it may yield contradictory results, depending on the meaning assigned to “randomness”. Jaynes claimed that symmetry requirements solve the paradox by selecting a unique solution to the problem. I show that this is not the case and that every variant obtained from the principle of indifference can also be obtained from Jaynes’ principle of transformation groups. This is because (...)
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  33. Collaboration in Scientific Practice—-A Social Epistemology of Research Groups.Susann Wagenknecht - 2014 - Dissertation, Aarhus University
    This monograph investigates the collaborative creation of scientific knowledge in research groups. To do so, I combine philosophical analysis with a first-hand comparative case study of two research groups in experimental science. Qualitative data are gained through observation and interviews, and I combine empirical insights with existing approaches to knowledge creation in philosophy of science and social epistemology. -/- On the basis of my empirically-grounded analysis I make several conceptual contributions. I study scientific collaboration as the interaction of (...)
     
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  34.  34
    Decidability and Computability of Certain Torsion-Free Abelian Groups.Rodney G. Downey, Sergei S. Goncharov, Asher M. Kach, Julia F. Knight, Oleg V. Kudinov, Alexander G. Melnikov & Daniel Turetsky - 2010 - Notre Dame Journal of Formal Logic 51 (1):85-96.
    We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.
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  35.  37
    Compact Domination for Groups Definable in Linear o-Minimal Structures.Pantelis E. Eleftheriou - 2009 - Archive for Mathematical Logic 48 (7):607-623.
    We prove the Compact Domination Conjecture for groups definable in linear o-minimal structures. Namely, we show that every definably compact group G definable in a saturated linear o-minimal expansion of an ordered group is compactly dominated by (G/G 00, m, π), where m is the Haar measure on G/G 00 and π : G → G/G 00 is the canonical group homomorphism.
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  36.  25
    An Elementary Presentation of the Equivalence Between MV-Algebras and L-Groups with Strong Unit.Roberto Cignoli & Daniele Mundici - 1998 - Studia Logica 61 (1):49-64.
    Aim of this paper is to provide a self-contained presentation of the natural equivalence between MV-algebras and lattice-ordered abelian groups with strong unit.
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  37.  58
    Religious Hatred Laws: Protecting Groups or Belief?Eric Barendt - 2011 - Res Publica 17 (1):41-53.
    This article examines the issues raised by recent legislation proscribing incitement to religious hatred. In particular, it examines how far arguments for prohibiting racist hate speech apply also to the prohibition of religious hate speech. It identifies a number of significant differences between race and religion. It also examines several questions raised by the prohibition of religious hate speech, including the meaning and scope of religious identity, why that identity should receive special protection, and whether protection should be directed to (...)
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  38.  87
    One-Basedness and Groups of the Form G/G 00.Davide Penazzi - 2011 - Archive for Mathematical Logic 50 (7-8):743-758.
    We initiate a geometric stability study of groups of the form G/G 00, where G is a 1-dimensional definably compact, definably connected, definable group in a real closed field M. We consider an enriched structure M′ with a predicate for G 00 and check 1-basedness or non-1-basedness for G/G 00, where G is an additive truncation of M, a multiplicative truncation of M, SO 2(M) or one of its truncations; such groups G/G 00 are now interpretable in M′. (...)
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  39.  5
    Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups.Larsen Louder, Chloé Perin & Rizos Sklinos - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):521-539.
    We use hyperbolic towers to answer some model-theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type $p_{0}$ but that there is a finitely generated model which omits $p^{}_{0}$. We exhibit a finitely generated model in which there are two maximal independent sets of realizations of the generic type which have different cardinalities. We also show that a free product of homogeneous (...) is not necessarily homogeneous. (shrink)
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  40.  47
    Animal Groups and Social Ontology: An Argument From the Phenomenology of Behavior.Alejandro Arango - 2016 - Phenomenology and the Cognitive Sciences 15 (3):403-422.
    Through a critical engagement with Merleau-Ponty’s discussion of the concepts of nature, life, and behavior, and with contemporary accounts of animal groups, this article argues that animal groups exhibit sociality and that sociality is a fundamental ontological condition. I situate my account in relation to the superorganism and selfish individual accounts of animal groups in recent biology and zoology. I argue that both accounts are inadequate. I propose an alternative account of animal groups and animal sociality (...)
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  41.  15
    Completely Metrisable Groups Acting on Trees.Christian Rosendal - 2011 - Journal of Symbolic Logic 76 (3):1005 - 1022.
    We consider actions of completely metrisable groups on simplicial trees in the context of the Bass—Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild conditions on a completely metrisable group G, namely, that the set of elements generating a non-discrete or finite subgroup is somewhere dense, we show that in any decomposition as a free product with amalgamation, G = A * C B, the amalgamated groups A, B (...)
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  42.  12
    Interest Groups and Pro-Animal Rights Legislation.Brenda J. Lutz & James M. Lutz - 2011 - Society and Animals 19 (3):261-277.
    The American states have demonstrated varying levels of support for animal rights legislation. The activities of interest groups, including pressures from competing groups, help to explain the presence or absence of ten pro-animal regulations and laws. This article analyzes and ranks each of the fifty states with regard to ten key areas of animal protection and welfare legislation. The analysis reveals that states with a more agricultural economic base are less likely to provide protection to animals. In addition, (...)
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  43.  59
    The Compensatory Rights of Emerging Interest Groups.Edmund F. Byrne - 1993 - Social Philosophy Today 8:397-416.
    Author argues that an emerging interest group, especially one that seeks to reverse past discrimination against its predecessors in the public arena, is entitled to enhanced consideration as a means of achieving long denied but merited rights. First this thesis is defended by identifying both practical need and theoretical support for emerging interest groups. Then these findings are applied specifically to the rights of women as an emerging interest group. (Publisher left off last word of title: 'Groups'.).
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  44.  9
    Monadic MV-Algebras Are Equivalent to Monadic ℓ-Groups with Strong Unit.C. Cimadamore & J. P. Díaz Varela - 2011 - Studia Logica 98 (1-2):175-201.
    In this paper we extend Mundici’s functor Γ to the category of monadic MV-algebras. More precisely, we define monadic ℓ -groups and we establish a natural equivalence between the category of monadic MV-algebras and the category of monadic ℓ -groups with strong unit. Some applications are given thereof.
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  45.  1
    Coxeter Groups and Abstract Elementary Classes: The Right-Angled Case.Tapani Hyttinen & Gianluca Paolini - 2019 - Notre Dame Journal of Formal Logic 60 (4):707-731.
    We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes, for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these results (...)
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  46.  73
    Toleration and Informal Groups: How Does the Formal Dimension Affect Groups' Capacity to Tolerate?F. Zuolo - 2013 - European Journal of Political Theory 12 (3):288-305.
    The ‘agents’ of toleration can be divided into three categories: public institutions, groups and individuals. If it is mostly accepted that both public institutions and individuals are capable of toleration, it is not clear that such a capacity can be attributed to groups, although in daily discourse we seem ready to say that a certain social group is (in)tolerant. This article aims to address this issue by investigating the relationship between collective agency and social groups. Formal (...) (e.g. corporations) have internal rules and collectively recognized decision-making procedures that constitute a collective behaviour. However, it is not clear if and in what sense such a capacity is also upheld by informal groups. This article discusses some competing criteria to define informal groups and proposes the shared convictions criterion. In conclusion, this criterion is applied to toleration-related issues, so as to reconcile our ordinary understanding of groups’ toleration with a more technical analysis. (shrink)
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  47.  71
    Non-Standard Lattices and o-Minimal Groups.Pantelis E. Eleftheriou - 2013 - Bulletin of Symbolic Logic 19 (1):56-76.
    We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invariant of the group at hand. The analysis first goes through a local level, where a pertinent notion of (...)
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  48.  43
    Invariance Results for Definable Extensions of Groups.Mário J. Edmundo, Gareth O. Jones & Nicholas J. Peatfield - 2011 - Archive for Mathematical Logic 50 (1-2):19-31.
    We show that in an o-minimal expansion of an ordered group finite definable extensions of a definable group which is defined in a reduct are already defined in the reduct. A similar result is proved for finite topological extensions of definable groups defined in o-minimal expansions of the ordered set of real numbers.
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  49.  35
    On Some Sheaves of Special Groups.Vincent Astier - 2007 - Archive for Mathematical Logic 46 (5-6):481-488.
    Using sheaves of special groups, we show that a general local-global principle holds for every reduced special group whose associated space of orderings only has a finite number of accumulation points. We also compute the behaviour of the Boolean hull functor applied to sheaves of special groups.
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  50.  7
    On Preservation of Stability for Finite Extensions of Abelian Groups.Frieder Haug - 1994 - Mathematical Logic Quarterly 40 (1):14-26.
    We characterize preservation of superstability and ω-stability for finite extensions of abelian groups and reduce the general case to the case of p-groups. In particular we study finite extensions of divisible abelian groups. We prove that superstable abelian-by-finite groups have only finitely many conjugacy classes of Sylow p-subgroups.
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