Search results for 'Finite' (try it on Scholar)

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  1. David J. Chalmers (1996). Does a Rock Implement Every Finite-State Automaton? Synthese 108 (3):309-33.
    Hilary Putnam has argued that computational functionalism cannot serve as a foundation for the study of the mind, as every ordinary open physical system implements every finite-state automaton. I argue that Putnam's argument fails, but that it points out the need for a better understanding of the bridge between the theory of computation and the theory of physical systems: the relation of implementation. It also raises questions about the class of automata that can serve as a basis for understanding (...)
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  2.  9
    Jean-Luc Nancy (2003). A Finite Thinking. Stanford University Press.
    This book is a rich collection of philosophical essays radically interrogating key notions and preoccupations of the phenomenological tradition. While using Heidegger’s Being and Time as its permanent point of reference and dispute, this collection also confronts other important philosophers, such as Kant, Nietzsche, and Derrida. The projects of these pivotal thinkers of finitude are relentlessly pushed to their extreme, with respect both to their unexpected horizons and to their as yet unexplored analytical potential. A Finite Thinking shows (...)
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  3.  10
    Jonas R. Becker Arenhart (2012). Finite Cardinals in Quasi-Set Theory. Studia Logica 100 (3):437-452.
    Quasi-set theory is a ZFU-like axiomatic set theory, which deals with two kinds of ur-elements: M-atoms, objects like the atoms of ZFU, and m-atoms, items for which the usual identity relation is not defined. One of the motivations to advance such a theory is to deal properly with collections of items like particles in non-relativistic quantum mechanics when these are understood as being non-individuals in the sense that they may be indistinguishable although identity does not apply to them. According to (...)
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  4.  59
    David Ellerman, On Classical Finite Probability Theory as a Quantum Probability Calculus.
    This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. The (...)
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  5. Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto (1996). Almost Everywhere Equivalence of Logics in Finite Model Theory. Bulletin of Symbolic Logic 2 (4):422-443.
    We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L ′ are two logics and μ is an asymptotic measure on finite structures, then $\scr{L}\equiv _{\text{a.e.}}\scr{L}^{\prime}(\mu)$ means that there is a class C of (...) structures with μ (C)=1 and such that L and L ′ define the same queries on C. We carry out a systematic investigation of $\equiv _{\text{a.e.}}$ with respect to the uniform measure and analyze the $\equiv _{\text{a.e.}}$ -equivalence classes of several logics that have been studied extensively in finite model theory. Moreover, we explore connections with descriptive complexity theory and examine the status of certain classical results of model theory in the context of this new framework. (shrink)
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  6.  20
    Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach (1998). Labeled Calculi and Finite-Valued Logics. Studia Logica 61 (1):7-33.
    A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite-valued logic if the labels are interpreted as sets of truth values (sets-as-signs). Furthermore, it is shown that any finite-valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is (...)
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  7.  39
    Olivier Finkel (2008). Topological Complexity of Locally Finite Ω-Languages. Archive for Mathematical Logic 47 (6):625-651.
    Locally finite omega languages were introduced by Ressayre [Formal languages defined by the underlying structure of their words. J Symb Log 53(4):1009–1026, 1988]. These languages are defined by local sentences and extend ω-languages accepted by Büchi automata or defined by monadic second order sentences. We investigate their topological complexity. All locally finite ω-languages are analytic sets, the class LOC ω of locally finite ω-languages meets all finite levels of the Borel hierarchy and there exist some locally (...)
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  8.  7
    Laurence Kirby (2008). A Hierarchy of Hereditarily Finite Sets. Archive for Mathematical Logic 47 (2):143-157.
    This article defines a hierarchy on the hereditarily finite sets which reflects the way sets are built up from the empty set by repeated adjunction, the addition to an already existing set of a single new element drawn from the already existing sets. The structure of the lowest levels of this hierarchy is examined, and some results are obtained about the cardinalities of levels of the hierarchy.
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  9.  5
    Gerd Sebald (2011). Crossing the Finite Provinces of Meaning. Experience and Metaphor. Human Studies 34 (4):341-352.
    Schutz’s references to literature and arts in his theoretical works are manifold. But literature and theory are both a certain kind of a finite province of meaning, that means they are not easily accessible from the paramount reality of everyday life. Now there is another kind of referring to literature: metaphorizing it. Using it, as may be said with Lakoff and Johnson, to understand and to experience one kind of thing in terms of another. Literally metapherein means “to carry (...)
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  10.  13
    Ehud Hrushovski (2013). On Pseudo-Finite Dimensions. Notre Dame Journal of Formal Logic 54 (3-4):463-495.
    We attempt to formulate issues around modularity and Zilber’s trichotomy in a setting that intersects additive combinatorics. In particular, we update the open problems on quasi-finite structures from [9].
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  11.  19
    Ian Hodkinson & Martin Otto (2003). Finite Conformal Hypergraph Covers and Gaifman Cliques in Finite Structures. Bulletin of Symbolic Logic 9 (3):387-405.
    We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques-thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a (...) conformal hypergraph. In terms of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of first-order logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF. (shrink)
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  12.  3
    Laurence Kirby (2010). Substandard Models of Finite Set Theory. Mathematical Logic Quarterly 56 (6):631-642.
    A survey of the isomorphic submodels of Vω, the set of hereditarily finite sets. In the usual language of set theory, Vω has 2ℵ0 isomorphic submodels. But other set-theoretic languages give different systems of submodels. For example, the language of adjunction allows only countably many isomorphic submodels of Vω.
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  13.  8
    Wojciech Buszkowski (2002). Finite Models of Some Substructural Logics. Mathematical Logic Quarterly 48 (1):63-72.
    We give a proof of the finite model property of some fragments of commutative and noncommutative linear logic: the Lambek calculus, BCI, BCK and their enrichments, MALL and Cyclic MALL. We essentially simplify the method used in [4] for proving fmp of BCI and the Lambek ca culus and in [5] for proving fmp of MALL. Our construction of finite models also differs from that used in Lafont [8] in his proof of fmp of MALL.
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  14.  12
    Ross Willard (2000). A Finite Basis Theorem for Residually Finite, Congruence Meet-Semidistributive Varieties. Journal of Symbolic Logic 65 (1):187-200.
    We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then it is finitely based. Theorem B: there is an algorithm which, given $m and a finite algebra in a finite language, determines whether the variety generated by the algebra is congruence meet-semidistributive and residually less than m.
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  15.  6
    Sven Ove Hansson (2012). Finite Contractions on Infinite Belief Sets. Studia Logica 100 (5):907-920.
    Contractions on belief sets that have no finite representation cannot be finite in the sense that only a finite number of sentences is removed. However, such contractions can be delimited so that the actual change takes place in a logically isolated, finite-based part of the belief set. A construction that answers to this principle is introduced, and is axiomatically characterized. It turns out to coincide with specified meet contraction.
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  16.  20
    Eric Rosen (1997). Modal Logic Over Finite Structures. Journal of Logic, Language and Information 6 (4):427-439.
    We investigate properties of propositional modal logic over the classof finite structures. In particular, we show that certain knownpreservation theorems remain true over this class. We prove that aclass of finite models is defined by a first-order sentence and closedunder bisimulations if and only if it is definable by a modal formula.We also prove that a class of finite models defined by a modal formulais closed under extensions if and only if it is defined by a -modal (...)
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  17.  53
    Panu Raatikainen (2000). The Concept of Truth in a Finite Universe. Journal of Philosophical Logic 29 (6):617-633.
    The prospects and limitations of defining truth in a finite model in the same language whose truth one is considering are thoroughly examined. It is shown that in contradistinction to Tarski's undefinability theorem for arithmetic, it is in a definite sense possible in this case to define truth in the very language whose truth is in question.
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  18.  19
    Randolph Sloof (2004). Finite Horizon Bargaining With Outside Options And Threat Points. Theory and Decision 57 (2):109-142.
    We characterize equilibrium behavior in a finite horizon multiple-pie alternating offer bargaining game in which both agents have outside options and threat points. In contrast to the infinite horizon case the strength of the threat to delay agreement is non-stationary and decreases over time. Typically the delay threat determines equilibrium proposals in early periods, while the threat to opt out characterizes those in later ones. Owing to this non-stationarity both threats may appear in the equilibrium shares immediately agreed upon (...)
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  19.  7
    Merrie Bergmann (2005). Finite Tree Property for First-Order Logic with Identity and Functions. Notre Dame Journal of Formal Logic 46 (2):173-180.
    The typical rules for truth-trees for first-order logic without functions can fail to generate finite branches for formulas that have finite models–the rule set fails to have the finite tree property. In 1984 Boolos showed that a new rule set proposed by Burgess does have this property. In this paper we address a similar problem with the typical rule set for first-order logic with identity and functions, proposing a new rule set that does have the finite (...)
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  20.  25
    Michał Kozak (2009). Distributive Full Lambek Calculus has the Finite Model Property. Studia Logica 91 (2):201 - 216.
    We prove the Finite Model Property (FMP) for Distributive Full Lambek Calculus ( DFL ) whose algebraic semantics is the class of distributive residuated lattices ( DRL ). The problem was left open in [8, 5]. We use the method of nuclei and quasi–embedding in the style of [10, 1].
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  21.  25
    Arnon Avron, Jonathan Ben-Naim & Beata Konikowska (2007). Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics. Logica Universalis 1 (1):41-70.
    . The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the (...)
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  22.  11
    Leendert Huisman (2015). Reflecting on Finite Additivity. Synthese 192 (6):1785-1797.
    An infinite lottery experiment seems to indicate that Bayesian conditionalization may be inconsistent when the prior credence function is finitely additive because, in that experiment, it conflicts with the principle of reflection. I will show that any other form of updating credences would produce the same conflict, and, furthermore, that the conflict is not between conditionalization and reflection but, instead, between finite additivity and reflection. A correct treatment of the infinite lottery experiment requires a careful treatment of finite (...)
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  23.  27
    Raymond J. Nelson (1975). Behaviorism, Finite Automata, and Stimulus-Response Theory. Theory and Decision 6 (August):249-67.
    In this paper it is argued that certain stimulus-response learning models which are adequate to represent finite automata (acceptors) are not adequate to represent noninitial state input-output automata (transducers). This circumstance suggests the question whether or not the behavior of animals if satisfactorily modelled by automata is predictive. It is argued in partial answer that there are automata which can be explained in the sense that their transition and output functions can be described (roughly, Hempel-type covering law explanation) while (...)
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  24.  12
    Anuj Dawar, Kees Doets, Steven Lindell & Scott Weinstein (1998). Elementary Properties of the Finite Ranks. Mathematical Logic Quarterly 44 (3):349-353.
    This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first-order definable over the class of finite directed graphs and that this class admits a first-order definable global linear order. We apply this last result to show that FO = FO.
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  25.  8
    Fraser Macbride (2000). On Finite Hume. Philosophia Mathematica 8 (2):150-159.
    Neo-Fregeanism contends that knowledge of arithmetic may be acquired by second-order logical reflection upon Hume's principle. Heck argues that Hume's principle doesn't inform ordinary arithmetical reasoning and so knowledge derived from it cannot be genuinely arithmetical. To suppose otherwise, Heck claims, is to fail to comprehend the magnitude of Cantor's conceptual contribution to mathematics. Heck recommends that finite Hume's principle be employed instead to generate arithmetical knowledge. But a better understanding of Cantor's contribution is achieved if it is supposed (...)
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  26.  2
    Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner (1999). On Finite Model Property for Admissible Rules. Mathematical Logic Quarterly 45 (4):505-520.
    Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 (...)
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  27.  34
    M. Krynicki & K. Zdanowski (2005). Theories of Arithmetics in Finite Models. Journal of Symbolic Logic 70 (1):1-28.
    We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ₂—theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ₁—theory of multiplication and order is decidable in finite (...)
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  28.  11
    Jay Newhard (2004). Disquotationalism, Minimalism, and the Finite Minimal Theory. Canadian Journal of Philosophy 34 (1):61 - 86.
    Recently, Paul Horwich has developed the minimalist theory of truth, according to which the truth predicate does not express a substantive property, though it may be used as a grammatical expedient. Minimalism shares these claims with Quine’s disquotationalism; it differs from disquotationalism primarily in holding that truth-bearers are propositions, rather than sentences. Despite potential ontological worries, allowing that propositions bear truth gives Horwich a prima facie response to several important objections to disquotationalism. In section I of this paper, disquotationalism is (...)
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  29.  5
    Georg Gottlob (1997). Relativized Logspace and Generalized Quantifiers Over Finite Ordered Structures. Journal of Symbolic Logic 62 (2):545-574.
    We here examine the expressive power of first order logic with generalized quantifiers over finite ordered structures. In particular, we address the following problem: Given a family Q of generalized quantifiers expressing a complexity class C, what is the expressive power of first order logic FO(Q) extended by the quantifiers in Q? From previously studied examples, one would expect that FO(Q) captures L C , i.e., logarithmic space relativized to an oracle in C. We show that this is (...)
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  30.  1
    Ai‐ni Hsieh & James G. Raftery (2006). A Finite Model Property for RMImin. Mathematical Logic Quarterly 52 (6):602-612.
    It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMImin has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMImin is decidable.
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  31.  12
    Ronnie Hermens (2014). Conway–Kochen and the Finite Precision Loophole. Foundations of Physics 44 (10):1038-1048.
    Recently Cator and Landsman made a comparison between Bell’s Theorem and Conway and Kochen’s Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway–Kochen Theorem has been performed thus far, and, secondly, because the Conway–Kochen Theorem is strongly connected to the Kochen–Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. (...)
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  32.  2
    C. J. van Alten (2005). The Finite Model Property for Knotted Extensions of Propositional Linear Logic. Journal of Symbolic Logic 70 (1):84-98.
    The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: γ, xn → y / γ, xm → y. It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the (...)
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  33.  3
    Michael D. Barber (forthcoming). Resistance to Pragmatic Tendencies in the World of Working in the Religious Finite Province of Meaning. Human Studies:1-24.
    This essay describes some of the basic pragmatic tendencies at work in the world of working and then shows how the finite provinces of meaning of theoretical contemplation and literature act against those pragmatic tendencies. This analysis prepares the way to see how the religious province of meaning in a similar but also distinctive way acts back against these pragmatic tendencies. These three finite provinces of meaning make it possible to see the world from another center of orientation (...)
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  34.  16
    Stan Gudder (2006). Quantum Mechanics on Finite Groups. Foundations of Physics 36 (8):1160-1192.
    Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements in (...)
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  35.  5
    Arnold W. Miller (2011). A Dedekind Finite Borel Set. Archive for Mathematical Logic 50 (1-2):1-17.
    In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if ${B\subseteq 2^\omega}$ is a G δσ -set then either B is countable or B contains a perfect subset. Second, we prove that if 2 ω is the countable union of countable sets, then there exists an F σδ set ${C\subseteq 2^\omega}$ such that C is uncountable but contains no perfect subset. Finally, (...)
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  36.  15
    Pierre Cartier (2012). How to Take Advantage of the Blur Between the Finite and the Infinite. Logica Universalis 6 (1-2):217-226.
    In this paper is presented and discussed the notion of true finite by opposition to the notion of theoretical finite. Examples from mathematics and physics are given. Fermat’s infinite descent principle is challenged.
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  37.  7
    John Krueger (2014). Strongly Adequate Sets and Adding a Club with Finite Conditions. Archive for Mathematical Logic 53 (1-2):119-136.
    We continue the study of adequate sets which we began in (Krueger in Forcing with adequate sets of models as side conditions) by introducing the idea of a strongly adequate set, which has an additional requirement on the overlap of two models past their comparison point. We present a forcing poset for adding a club to a fat stationary subset of ω 2 with finite conditions, thereby showing that a version of the forcing posets of Friedman (Set theory: Centre (...)
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  38.  4
    Martin Grohe (1996). Some Remarks on Finite Löwenheim‐Skolem Theorems. Mathematical Logic Quarterly 42 (1):569-571.
    We discuss several possible extensions of the classical Löwenheim-Skolem Theorem to finite structures and give a counterexample refuting almost all of them.
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  39.  10
    Shawn Hedman & Wai Yan Pong (2011). Quantifier-Eliminable Locally Finite Graphs. Mathematical Logic Quarterly 57 (2):180-185.
    We identify the locally finite graphs that are quantifier-eliminable and their first order theories in the signature of distance predicates. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  40.  8
    Murdoch J. Gabbay (2012). Finite and Infinite Support in Nominal Algebra and Logic: Nominal Completeness Theorems for Free. Journal of Symbolic Logic 77 (3):828-852.
    By operations on models we show how to relate completeness with respect to permissivenominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal models, so the construction hinges on generating from an instance of the latter, some instance of the former in which sufficiently many inequalities are preserved between elements. We do this using an infinite generalisation of nominal atoms-abstraction. The results are of interest in their (...)
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  41.  20
    Cédric Dégremont & Nina Gierasimczuk (2011). Finite Identification From the Viewpoint of Epistemic Update. Information And Computation 209 (3):383-396.
    Formal learning theory constitutes an attempt to describe and explain the phenomenon of learning, in particular of language acquisition. The considerations in this domain are also applicable in philosophy of science, where it can be interpreted as a description of the process of scientific inquiry. The theory focuses on various properties of the process of hypothesis change over time. Treating conjectures as informational states, we link the process of conjecture-change to epistemic update. We reconstruct and analyze the temporal aspect of (...)
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  42.  6
    Pimpen Vejjajiva & Supakun Panasawatwong (2014). A Note on Weakly Dedekind Finite Sets. Notre Dame Journal of Formal Logic 55 (3):413-417.
    A set $A$ is Dedekind infinite if there is a one-to-one function from $\omega$ into $A$. A set $A$ is weakly Dedekind infinite if there is a function from $A$ onto $\omega$; otherwise $A$ is weakly Dedekind finite. For a set $M$, let $\operatorname{dfin}^{*}$ denote the set of all weakly Dedekind finite subsets of $M$. In this paper, we prove, in Zermelo–Fraenkel set theory, that $|\operatorname{dfin}^{*}|\lt |\mathcal{P}|$ if $\operatorname{dfin}^{*}$ is Dedekind infinite, whereas $|\operatorname{dfin}^{*}|\lt |\mathcal{P}|$ cannot be proved from (...)
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  43.  6
    T. Lee (2003). Arithmetical Definability Over Finite Structures. Mathematical Logic Quarterly 49 (4):385.
    Arithmetical definability has been extensively studied over the natural numbers. In this paper, we take up the study of arithmetical definability over finite structures, motivated by the correspondence between uniform AC0 and FO. We prove finite analogs of three classic results in arithmetical definability, namely that < and TIMES can first-order define PLUS, that < and DIVIDES can first-order define TIMES, and that < and COPRIME can first-order define TIMES. The first result sharpens the equivalence FO =FO to (...)
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  44. Annalisa Marcja & Carlo Toffalori (1994). Abelian‐by‐G Groups, for G Finite, From the Model Theoretic Point of View. Mathematical Logic Quarterly 40 (1):125-131.
    Let G be a finite group. We prove that the theory af abelian-by-G groups is decidable if and only if the theory of modules over the group ring ℤ[G] is decidable. Then we study some model theoretic questions about abelian-by-G groups, in particular we show that their class is elementary when the order of G is squarefree.
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  45.  2
    A. E. Wasilewska & M. Mostowski (2004). Arithmetic of Divisibility in Finite Models. Mathematical Logic Quarterly 50 (2):169.
    We prove that the finite-model version of arithmetic with the divisibility relation is undecidable . Additionally we prove FM-representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤0′. We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only.
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  46.  5
    Matthew Smedberg (2013). A Dense Family of Well-Behaved Finite Monogenerated Left-Distributive Groupoids. Archive for Mathematical Logic 52 (3-4):377-402.
    We construct a family $\fancyscript{F}$ , indexed by five integer parameters, of finite monogenerated left-distributive (LD) groupoids with the property that every finite monogenerated LD groupoid is a quotient of a member of $\fancyscript{F}$ . The combinatorial abundance of finite monogenerated LD groupoids is encoded in the congruence lattices of the groupoids $\fancyscript{F}$ , which we show to be extremely large.
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  47.  5
    Frank Wagner (2001). Fields of Finite Morley Rank. Journal of Symbolic Logic 66 (2):703-706.
    If K is a field of finite Morley rank, then for any parameter set $A \subseteq K^{eq}$ the prime model over A is equal to the model-theoretic algebraic closure of A. A field of finite Morley rank eliminates imaginaries. Simlar results hold for minimal groups of finite Morley rank with infinite acl( $\emptyset$ ).
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  48.  13
    Ross Willard (1994). Hereditary Undecidability of Some Theories of Finite Structures. Journal of Symbolic Logic 59 (4):1254-1262.
    Using a result of Gurevich and Lewis on the word problem for finite semigroups, we give short proofs that the following theories are hereditarily undecidable: (1) finite graphs of vertex-degree at most 3; (2) finite nonvoid sets with two distinguished permutations; (3) finite-dimensional vector spaces over a finite field with two distinguished endomorphisms.
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  49.  12
    M. Carmen Sánchez (1998). Rational Choice on Non-Finite Sets by Means of Expansion-Contraction Axioms. Theory and Decision 45 (1):1-17.
    The rationalization of a choice function, in terms of assumptions that involve expansion or contraction properties of the feasible set, over non-finite sets is analyzed. Schwartz's results, stated in the finite case, are extended to this more general framework. Moreover, a characterization result when continuity conditions are imposed on the choice function, as well as on the binary relation that rationalizes it, is presented.
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  50.  3
    Takahito Aoto & Hiroyuki Shirasu (1999). On the Finite Model Property of Intuitionistic Modal Logics Over MIPC. Mathematical Logic Quarterly 45 (4):435-448.
    MIPC is a well-known intuitionistic modal logic of Prior and Bull . It is shown that every normal intuitionistic modal logic L over MIPC has the finite model property whenever L is Kripke-complete and universal.
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