Search results for 's4 axiom' (try it on Scholar)

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  1. Susanne Bobzien (2012). If It's Clear, Then It's Clear That It's Clear, or is It? Higher-Order Vagueness and the S4 Axiom. In B. Morison K. Ierodiakonou (ed.), Episteme, etc. OUP UK.score: 63.0
    The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity (...)
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  2. Thomas Mormann, McKinsey Algebras and Topological Models of S4.1.score: 45.0
    The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that can be used to (...)
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  3. Timothy Williamson (1995). Does Assertibility Satisfy the S4 Axiom? Crítica 27 (81):3 - 25.score: 45.0
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  4. R. I. Goldblatt (1973). Concerning the Proper Axiom for $S4.04$ and Some Related Systems. Notre Dame Journal of Formal Logic 14 (3):392-396.score: 36.0
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  5. R. I. Goldblatt (1975). Erratum: ``Concerning the Proper Axiom for $S4.04$ and Some Related Systems''. Notre Dame Journal of Formal Logic 16 (4):608-608.score: 36.0
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  6. Leo Simons (1962). A Reduction in the Number of Independent Axiom Schemata for $S4$. Notre Dame Journal of Formal Logic 3 (4):256-258.score: 36.0
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  7. Naoto Yonemitsu (1967). Review: Leo Simons, A Reduction in the Number of Independent Axiom Schemata for S4. [REVIEW] Journal of Symbolic Logic 32 (2):245-245.score: 36.0
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  8. Branden Fitelson (2002). Shortest Axiomatizations of Implicational S4 and S5. Notre Dame Journal of Formal Logic 43 (3):169-179.score: 27.0
    Shortest possible axiomatizations for the strict implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.
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  9. Zachary Ernst, Branden Fitelson, Kenneth Harris & Larry Wos (2002). Shortest Axiomatizations of Implicational S4 and S. Notre Dame Journal of Formal Logic 43 (3):169-179.score: 27.0
    Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.
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  10. Paul Corazza (2010). The Axiom of Infinity and Transformations J: V→V. Bulletin of Symbolic Logic 16 (1):37-84.score: 18.0
    We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals ought (...)
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  11. David W. Miller (2007). Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice. Logica Universalis 1 (1):183-199.score: 18.0
    . Dzik [2] gives a direct proof of the axiom of choice from the generalized Lindenbaum extension theorem LET. The converse is part of every decent logical education. Inspection of Dzik’s proof shows that its premise let attributes a very special version of the Lindenbaum extension property to a very special class of deductive systems, here called Dzik systems. The problem therefore arises of giving a direct proof, not using the axiom of choice, of the conditional . A (...)
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  12. Gemma Robles & José M. Méndez (2014). Curry's Paradox, Generalized Modus Ponens Axiom and Depth Relevance. Studia Logica 102 (1):185-217.score: 18.0
    “Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure ${\mathcal{M}_{\rm CL}}$ built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.
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  13. Peter Nyikos & Leszek Piątkiewicz (1995). On the Equivalence of Certain Consequences of the Proper Forcing Axiom. Journal of Symbolic Logic 60 (2):431-443.score: 18.0
    We prove that a number of axioms, each a consequence of PFA (the Proper Forcing Axiom) are equivalent. In particular we show that TOP (the Thinning-out Principle as introduced by Baumgartner in the Handbook of set-theoretic topology), is equivalent to the following statement: If I is an ideal on ω 1 with ω 1 generators, then there exists an uncountable $X \subseteq \omega_1$ , such that either [ X] ω ∩ I = ⊘ or $\lbrack X\rbrack^\omega \subseteq I$.
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  14. Samir Chopra, Aditya Ghose, Thomas Meyer & Ka-Shu Wong (2008). Iterated Belief Change and the Recovery Axiom. Journal of Philosophical Logic 37 (5):501 - 520.score: 18.0
    The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide (...)
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  15. David Bennett (2000). A Single Axiom for Set Theory. Notre Dame Journal of Formal Logic 41 (2):152-170.score: 18.0
    Axioms in set theory typically have the form , where is a relation which links with in some way. In this paper we introduce a particular linkage relation and a single axiom based on from which all the axioms of (Zermelo set theory) can be derived as theorems. The single axiom is presented both in informal and formal versions. This calls for some discussion of pertinent features of formal and informal axiomatic method and some discussion of pertinent features (...)
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  16. Olivier Esser (2000). Inconsistency of the Axiom of Choice with the Positive Theory GPK+ ∞. Journal of Symbolic Logic 65 (4):1911 - 1916.score: 18.0
    The idea of the positive theory is to avoid the Russell's paradox by postulating an axiom scheme of comprehension for formulas without "too much" negations. In this paper, we show that the axiom of choice is inconsistent with the positive theory GPK + ∞.
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  17. Jesse Alama (2013). The Simplest Axiom System for Hyperbolic Geometry Revisited, Again. Studia Logica:1-7.score: 18.0
    Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield two simpler axiom systems for absolute geometry.
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  18. Marianne Morillon (2010). Notions of Compactness for Special Subsets of ℝ I and Some Weak Forms of the Axiom of Choice. Journal of Symbolic Logic 75 (1):255-268.score: 18.0
    We work in set-theory without choice ZF. A set is Countable if it is finite or equipotent with ${\Bbb N}$ . Given a closed subset F of [0, 1] I which is a bounded subset of $\ell ^{1}(I)$ (resp. such that $F\subseteq c_{0}(I)$ ), we show that the countable axiom of choice for finite sets, (resp. the countable axiom of choice AC N ) implies that F is compact. This enhances previous results where AC N (resp. the (...) of Dependent Choices) was required. If I is linearly orderable (for example $I={\Bbb R}$ ), then, in ZF, the closed unit ball of the Hilbert space $\ell ^{2}(I)$ is (Loeb-)compact in the weak topology. However, the weak compactness of the closed unit ball of $\ell ^{2}(\scr{P}({\Bbb R}))$ is not provable in ZF. (shrink)
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  19. Paul Corazza (2000). Consistency of V = HOD with the Wholeness Axiom. Archive for Mathematical Logic 39 (3):219-226.score: 18.0
    The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language $\{\in,j\}$ , and that asserts the existence of a nontrivial elementary embedding $j:V\to V$ . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an $I_1$ embedding. This answers a question (...)
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  20. Kyriakos Keremedis (2001). Disasters in Topology Without the Axiom of Choice. Archive for Mathematical Logic 40 (8):569-580.score: 18.0
    We show that some well known theorems in topology may not be true without the axiom of choice.
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  21. H. Montgomery & Richard Routley (1968). Non-Contingency Axioms for S4 and S5. Logique Et Analyse 11:422-424.score: 18.0
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  22. Greg Oman (2010). On the Axiom of Union. Archive for Mathematical Logic 49 (3):283-289.score: 18.0
    In this paper, we study the union axiom of ZFC. After a brief introduction, we sketch a proof of the folklore result that union is independent of the other axioms of ZFC. In the third section, we prove some results in the theory T:= ZFC minus union. Finally, we show that the consistency of T plus the existence of an inaccessible cardinal proves the consistency of ZFC.
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  23. Victor Pambuccian (2011). The Simplest Axiom System for Plane Hyperbolic Geometry Revisited. Studia Logica 97 (3):347 - 349.score: 18.0
    Using the axiom system provided by Carsten Augat in [1], it is shown that the only 6-variable statement among the axioms of the axiom system for plane hyperbolic geometry (in Tarski's language L B =), we had provided in [3], is superfluous. The resulting axiom system is the simplest possible one, in the sense that each axiom is a statement in prenex form about at most 5 points, and there is no axiom system consisting entirely (...)
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  24. A. N. Prior (1957). Review: Arata Ishimoto, A Note on the Paper "A Set of Axioms of the Modal Propositional Calculus Equivalent to S3."; Arata Ishimoto, A Formulation of the Modal Propositional Calculus Equivalent to S4. [REVIEW] Journal of Symbolic Logic 22 (3):326-327.score: 18.0
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  25. Gemma Robles & José M. Méndez (2010). Axiomatizing S4+ and J+ Without the Suffixing, Prefixing and Self-Distribution of the Conditional Axioms. Bulletin of the Section of Logic 39 (1/2):79-91.score: 18.0
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  26. Donald Paul Snyder (1973). Review: J. Jay Zeman, Bases for S4 and S4.2 Without Added Axioms. [REVIEW] Journal of Symbolic Logic 38 (2):328-328.score: 18.0
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  27. Teruyuki Yorioka (2008). Some Weak Fragments of Martin's Axiom Related to the Rectangle Refining Property. Archive for Mathematical Logic 47 (1):79-90.score: 18.0
    We introduce the anti-rectangle refining property for forcing notions and investigate fragments of Martin’s axiom for ℵ1 dense sets related to the anti-rectangle refining property, which is close to some fragment of Martin’s axiom for ℵ1 dense sets related to the rectangle refining property, and prove that they are really weaker fragments.
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  28. Huiling Zhu (2013). Distributive Proper Forcing Axiom and Cardinal Invariants. Archive for Mathematical Logic 52 (5-6):497-506.score: 18.0
    In this paper, we study the forcing axiom for the class of proper forcing notions which do not add ω sequence of ordinals. We study the relationship between this forcing axiom and many cardinal invariants. We use typical iterated forcing with large cardinals and analyse certain property being preserved in this process. Lastly, we apply the results to distinguish several forcing axioms.
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  29. John Bell (2008). The Axiom of Choice and the Law of Excluded Middle in Weak Set Theories. Mathematical Logic Quarterly 54 (2):194-201.score: 15.0
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  30. Wlodek Rabinowicz (1997). On Seidenfeld‘s Criticism of Sophisticated Violations of the Independence Axiom. Theory and Decision 43 (3):279-292.score: 15.0
    An agent who violates independence can avoid dynamic inconsistency in sequential choice if he is sophisticated enough to make use of backward induction in planning. However, Seidenfeld has demonstrated that such a sophisticated agent with dependent preferences is bound to violate the principle of dynamic substitution, according to which admissibility of a plan is preserved under substitution of indifferent options at various choice nodes in the decision tree. Since Seidenfeld considers dynamic substitution to be a coherence condition on dynamic choice, (...)
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  31. Kenneth Kunen & Dilip Raghavan (2009). Gregory Trees, the Continuum, and Martin's Axiom. Journal of Symbolic Logic 74 (2):712-720.score: 15.0
    We continue the investigation of Gregory trees and the Cantor Tree Property carried out by Hart and Kunen. We produce models of MA with the Continuum arbitrarily large in which there are Gregory trees, and in which there are no Gregory trees.
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  32. Norbert Brunner & Paul Howard (1992). Russell's Alternative to the Axiom of Choice. Mathematical Logic Quarterly 38 (1):529-534.score: 15.0
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  33. Christine Gaßner (1994). The Axiom of Choice in Second‐Order Predicate Logic. Mathematical Logic Quarterly 40 (4):533-546.score: 15.0
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  34. Arthur W. Apter (2011). Indestructibility, HOD, and the Ground Axiom. Mathematical Logic Quarterly 57 (3):261-265.score: 15.0
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  35. Stefano Baratella & Ruggero Ferro (1993). A Theory of Sets with the Negation of the Axiom of Infinity. Mathematical Logic Quarterly 39 (1):338-352.score: 15.0
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  36. Joaquín Borrego‐Díaz, Alejandro Fernández‐Margarit & Mario Pérez‐Jiménez (1996). On Overspill Principles and Axiom Schemes for Bounded Formulas. Mathematical Logic Quarterly 42 (1):341-348.score: 15.0
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  37. J. Brendle (2000). Martin's Axiom and the Dual Distributivity Number. Mathematical Logic Quarterly 46 (2):241-248.score: 15.0
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  38. Norbert Brunner & H. Reiju Mihara (2000). Arrow's Theorem, Weglorz' Models and the Axiom of Choice. Mathematical Logic Quarterly 46 (3):335-359.score: 15.0
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  39. Norbert Brunner, Karl Svozil & Matthias Baaz (1996). The Axiom of Choice in Quantum Theory. Mathematical Logic Quarterly 42 (1):319-340.score: 15.0
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  40. Timothy J. Carlson (2011). On the Conservativity of the Axiom of Choice Over Set Theory. Archive for Mathematical Logic 50 (7-8):777-790.score: 15.0
    We show that for various set theories T including ZF, T + AC is conservative over T for sentences of the form ${\forall x \exists ! y}$ A(x, y) where A(x, y) is a Δ0 formula.
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  41. Omar De la Cruz, Eric J. Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2008). Unions and the Axiom of Choice. Mathematical Logic Quarterly 54 (6):652-665.score: 15.0
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  42. W. Degen (2001). Rigit Unary Functions and the Axiom of Choice. Mathematical Logic Quarterly 47 (2):197-204.score: 15.0
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  43. Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2003). Metric Spaces and the Axiom of Choice. Mathematical Logic Quarterly 49 (5):455-466.score: 15.0
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  44. O. De la Cruz, Paul Howard & E. Hall (2002). Products of Compact Spaces and the Axiom of Choice. Mathematical Logic Quarterly 48 (4):508-516.score: 15.0
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  45. Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2003). Products of Compact Spaces and the Axiom of Choice II. Mathematical Logic Quarterly 49 (1):57-71.score: 15.0
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  46. Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Eleftherios Tachtsis (2005). Properties of the Real Line and Weak Forms of the Axiom of Choice. Mathematical Logic Quarterly 51 (6):598-609.score: 15.0
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  47. Peter L. Derks (1962). The Generality of the "Conditioning Axiom" in Human Binary Prediction. Journal of Experimental Psychology 63 (6):538.score: 15.0
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  48. Karl‐Heinz Diener (1994). A Remark on Ascending Chain Conditions, the Countable Axiom of Choice and the Principle of Dependent Choices. Mathematical Logic Quarterly 40 (3):415-421.score: 15.0
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  49. K. Diener (2000). On Kappa-Hereditary Sets and Consequences of the Axiom of Choice. Mathematical Logic Quarterly 46 (4):563-568.score: 15.0
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  50. Juliette Dodu & Marianne Morillon (1999). The Hahn-Banach Property and the Axiom of Choice. Mathematical Logic Quarterly 45 (3):299-314.score: 15.0
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