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.score: 24.0
    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. Panu Raatikainen (2000). The Concept of Truth in a Finite Universe. Journal of Philosophical Logic 29 (6):617-633.score: 24.0
    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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  3. Cédric Dégremont & Nina Gierasimczuk (2011). Finite Identification From the Viewpoint of Epistemic Update. Information And Computation 209 (3):383-396.score: 24.0
    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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  4. Ian Hodkinson & Martin Otto (2003). Finite Conformal Hypergraph Covers and Gaifman Cliques in Finite Structures. Bulletin of Symbolic Logic 9 (3):387-405.score: 24.0
    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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  5. Raymond J. Nelson (1975). Behaviorism, Finite Automata, and Stimulus-Response Theory. Theory and Decision 6 (August):249-67.score: 24.0
    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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  6. Michał Kozak (2009). Distributive Full Lambek Calculus has the Finite Model Property. Studia Logica 91 (2):201 - 216.score: 24.0
    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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  7. Eric Rosen (1997). Modal Logic Over Finite Structures. Journal of Logic, Language and Information 6 (4):427-439.score: 24.0
    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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  8. Jonas R. Becker Arenhart (2012). Finite Cardinals in Quasi-Set Theory. Studia Logica 100 (3):437-452.score: 24.0
    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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  9. Ehud Hrushovski (2013). On Pseudo-Finite Dimensions. Notre Dame Journal of Formal Logic 54 (3-4):463-495.score: 24.0
    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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  10. M. Krynicki & K. Zdanowski (2005). Theories of Arithmetics in Finite Models. Journal of Symbolic Logic 70 (1):1-28.score: 24.0
    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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  11. Ross Willard (2000). A Finite Basis Theorem for Residually Finite, Congruence Meet-Semidistributive Varieties. Journal of Symbolic Logic 65 (1):187-200.score: 24.0
    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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  12. Jean-Luc Nancy (2003). A Finite Thinking. Stanford University Press.score: 24.0
    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 that, (...)
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  13. Stan Gudder (2006). Quantum Mechanics on Finite Groups. Foundations of Physics 36 (8):1160-1192.score: 24.0
    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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  14. Jay Newhard (2004). Disquotationalism, Minimalism, and the Finite Minimal Theory. Canadian Journal of Philosophy 34 (1):61 - 86.score: 24.0
    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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  15. Sven Ove Hansson (2012). Finite Contractions on Infinite Belief Sets. Studia Logica 100 (5):907-920.score: 24.0
    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. 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.score: 24.0
    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 finite structures (...)
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  17. 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.score: 24.0
    . 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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  18. 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.score: 24.0
    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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  19. Erich Grädel, Phokion Kolaitis, Libkin G., Marx Leonid, Spencer Maarten, Vardi Joel, Y. Moshe, Yde Venema & Scott Weinstein (2007). Finite Model Theory and its Applications. Springer.score: 24.0
    This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, fixed-point, and (...)
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  20. Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach (1998). Labeled Calculi and Finite-Valued Logics. Studia Logica 61 (1):7-33.score: 24.0
    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 logarithmic in (...)
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  21. Mauro Gattari (2005). Finite and Physical Modalities. Notre Dame Journal of Formal Logic 46 (4):425-437.score: 24.0
    The logic Kf of the modalities of finite, devised to capture the notion of 'there exists a finite number of accessible worlds such that . . . is true', was introduced and axiomatized by Fattorosi. In this paper we enrich the logical framework of Kf: we give consistency properties and a tableau system (which yields the decidability) explicitly designed for Kf, and we introduce a shorter and more natural axiomatization. Moreover, we show the strong and suggestive relationship between (...)
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  22. Ross Willard (1994). Hereditary Undecidability of Some Theories of Finite Structures. Journal of Symbolic Logic 59 (4):1254-1262.score: 24.0
    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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  23. Pierre Cartier (2012). How to Take Advantage of the Blur Between the Finite and the Infinite. Logica Universalis 6 (1-2):217-226.score: 24.0
    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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  24. Gerd Sebald (2011). Crossing the Finite Provinces of Meaning. Experience and Metaphor. Human Studies 34 (4):341-352.score: 24.0
    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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  25. M. Carmen Sánchez (1998). Rational Choice on Non-Finite Sets by Means of Expansion-Contraction Axioms. Theory and Decision 45 (1):1-17.score: 24.0
    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 (1976), 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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  26. Georg Gottlob (1997). Relativized Logspace and Generalized Quantifiers Over Finite Ordered Structures. Journal of Symbolic Logic 62 (2):545-574.score: 24.0
    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 not (...)
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  27. Merrie Bergmann (2005). Finite Tree Property for First-Order Logic with Identity and Functions. Notre Dame Journal of Formal Logic 46 (2):173-180.score: 24.0
    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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  28. Pimpen Vejjajiva & Supakun Panasawatwong (2014). A Note on Weakly Dedekind Finite Sets. Notre Dame Journal of Formal Logic 55 (3):413-417.score: 24.0
    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 $\operatorname{dfin}^{*}(M)$ denote the set of all weakly Dedekind finite subsets of $M$. In this paper, we prove, in Zermelo–Fraenkel (ZF) set theory, that $|\operatorname{dfin}^{*}(M)|\lt |\mathcal{P}(M)|$ if $\operatorname{dfin}^{*}(M)$ is Dedekind infinite, whereas $|\operatorname{dfin}^{*}(M)|\lt |\mathcal{P}(M)|$ cannot be proved (...)
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  29. C. J. van Alten (2005). The Finite Model Property for Knotted Extensions of Propositional Linear Logic. Journal of Symbolic Logic 70 (1):84-98.score: 24.0
    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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  30. Ronnie Hermens (2014). Conway–Kochen and the Finite Precision Loophole. Foundations of Physics 44 (10):1038-1048.score: 24.0
    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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  31. Matthew Smedberg (2013). A Dense Family of Well-Behaved Finite Monogenerated Left-Distributive Groupoids. Archive for Mathematical Logic 52 (3-4):377-402.score: 24.0
    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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  32. Frank Wagner (2001). Fields of Finite Morley Rank. Journal of Symbolic Logic 66 (2):703-706.score: 24.0
    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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  33. Radosav Dordević, Miodrag Rašković & Zoran Ognjanović (2004). Completeness Theorem for Propositional Probabilistic Models Whose Measures Have Only Finite Ranges. Archive for Mathematical Logic 43 (4):557-563.score: 24.0
    A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P ≥s (with the intended meaning ‘‘the probability is at least s’’). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.
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  34. Olivier Finkel (2008). Topological Complexity of Locally Finite Ω-Languages. Archive for Mathematical Logic 47 (6):625-651.score: 24.0
    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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  35. Xingxing He, Jun Liu, Yang Xu, Luis Martínez & Da Ruan (2012). On Α-Satisfiability and its Α-Lock Resolution in a Finite Lattice-Valued Propositional Logic. Logic Journal of the Igpl 20 (3):579-588.score: 24.0
    Automated reasoning issues are addressed for a finite lattice-valued propositional logic LnP(X) with truth-values in a finite lattice-valued logical algebraic structure—lattice implication algebra. We investigate extended strategies and rules from classical logic to LnP(X) to simplify the procedure in the semantic level for testing the satisfiability of formulas in LnP(X) at a certain truth-value level α (α-satisfiability) while keeping the role of truth constant formula played in LnP(X). We propose a lock resolution method at a certain truth-value level (...)
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  36. Laurence Kirby (2008). A Hierarchy of Hereditarily Finite Sets. Archive for Mathematical Logic 47 (2):143-157.score: 24.0
    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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  37. John Krueger (2014). Strongly Adequate Sets and Adding a Club with Finite Conditions. Archive for Mathematical Logic 53 (1-2):119-136.score: 24.0
    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. Arnold W. Miller (2011). A Dedekind Finite Borel Set. Archive for Mathematical Logic 50 (1-2):1-17.score: 24.0
    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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  39. Randolph Sloof (2004). Finite Horizon Bargaining With Outside Options And Threat Points. Theory and Decision 57 (2):109-142.score: 24.0
    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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  40. Colin Howson (2013). Finite Additivity, Another Lottery Paradox and Conditionalisation. Synthese:1-24.score: 22.0
    In this paper I argue that de Finetti provided compelling reasons for rejecting countable additivity. It is ironical therefore that the main argument advanced by Bayesians against following his recommendation is based on the consistency criterion, coherence, he himself developed. I will show that this argument is mistaken. Nevertheless, there remain some counter-intuitive consequences of rejecting countable additivity, and one in particular has all the appearances of a full-blown paradox. I will end by arguing that in fact it is no (...)
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  41. San‐Min Wang (2013). The Finite Model Property for Semilinear Substructural Logics. Mathematical Logic Quarterly 59 (4-5):268-273.score: 21.0
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  42. Martin Grohe (1996). Some Remarks on Finite Löwenheim‐Skolem Theorems. Mathematical Logic Quarterly 42 (1):569-571.score: 21.0
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  43. Peter C. Fishburn (1990). Unique Nontransitive Measurement on Finite Sets. Theory and Decision 28 (1):21-46.score: 21.0
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  44. Shawn Hedman & Wai Yan Pong (2011). Quantifier-Eliminable Locally Finite Graphs. Mathematical Logic Quarterly 57 (2):180-185.score: 21.0
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  45. Laurence Kirby (2010). Substandard Models of Finite Set Theory. Mathematical Logic Quarterly 56 (6):631-642.score: 21.0
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  46. Takahito Aoto & Hiroyuki Shirasu (1999). On the Finite Model Property of Intuitionistic Modal Logics Over MIPC. Mathematical Logic Quarterly 45 (4):435-448.score: 21.0
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  47. Wojciech Buszkowski (2002). Finite Models of Some Substructural Logics. Mathematical Logic Quarterly 48 (1):63-72.score: 21.0
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  48. Anuj Dawar, Kees Doets, Steven Lindell & Scott Weinstein (1998). Elementary Properties of the Finite Ranks. Mathematical Logic Quarterly 44 (3):349-353.score: 21.0
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  49. B. Herrmann & W. Rautenberg (1992). Finite Replacement and Finite Hilbert‐Style Axiomatizability. Mathematical Logic Quarterly 38 (1):327-344.score: 21.0
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  50. Ai‐ni Hsieh & James G. Raftery (2006). A Finite Model Property for RMImin. Mathematical Logic Quarterly 52 (6):602-612.score: 21.0
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