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

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  1. Paul Corazza (2010). The Axiom of Infinity and Transformations J: V→V. Bulletin of Symbolic Logic 16 (1):37-84.score: 24.0
    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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  2. David W. Miller (2007). Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice. Logica Universalis 1 (1):183-199.score: 24.0
    . 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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  3. Gemma Robles & José M. Méndez (2014). Curry's Paradox, Generalized Modus Ponens Axiom and Depth Relevance. Studia Logica 102 (1):185-217.score: 24.0
    “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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  4. Olivier Esser (2000). Inconsistency of the Axiom of Choice with the Positive Theory GPK+ ∞. Journal of Symbolic Logic 65 (4):1911 - 1916.score: 24.0
    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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  5. 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: 24.0
    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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  6. Jesse Alama (2014). The Simplest Axiom System for Hyperbolic Geometry Revisited, Again. Studia Logica 102 (3):609-615.score: 24.0
    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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  7. David Bennett (2000). A Single Axiom for Set Theory. Notre Dame Journal of Formal Logic 41 (2):152-170.score: 24.0
    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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  8. 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: 24.0
    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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  9. 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: 24.0
    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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  10. 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: 24.0
    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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  11. Paul Corazza (2000). Consistency of V = HOD with the Wholeness Axiom. Archive for Mathematical Logic 39 (3):219-226.score: 24.0
    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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  12. Kyriakos Keremedis (2001). Disasters in Topology Without the Axiom of Choice. Archive for Mathematical Logic 40 (8):569-580.score: 24.0
    We show that some well known theorems in topology may not be true without the axiom of choice.
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  13. Greg Oman (2010). On the Axiom of Union. Archive for Mathematical Logic 49 (3):283-289.score: 24.0
    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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  14. Victor Pambuccian (2011). The Simplest Axiom System for Plane Hyperbolic Geometry Revisited. Studia Logica 97 (3):347 - 349.score: 24.0
    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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  15. Huiling Zhu (2013). Distributive Proper Forcing Axiom and Cardinal Invariants. Archive for Mathematical Logic 52 (5-6):497-506.score: 24.0
    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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  16. 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: 21.0
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  17. Kenneth Kunen & Dilip Raghavan (2009). Gregory Trees, the Continuum, and Martin's Axiom. Journal of Symbolic Logic 74 (2):712-720.score: 21.0
    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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  18. Wlodek Rabinowicz (1997). On Seidenfeld‘s Criticism of Sophisticated Violations of the Independence Axiom. Theory and Decision 43 (3):279-292.score: 21.0
    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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  19. Christine Gaßner (1994). The Axiom of Choice in Second‐Order Predicate Logic. Mathematical Logic Quarterly 40 (4):533-546.score: 21.0
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  20. E. Tachtsis & K. Keremedis (2001). Compact Metric Spaces and Weak Forms of the Axiom of Choice. Mathematical Logic Quarterly 47 (1):117-128.score: 21.0
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  21. 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: 21.0
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  22. 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: 21.0
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  23. K. Keremedis (2001). The Vector Space Kinna-Wagner Principle is Equivalent to the Axiom of Choice. Mathematical Logic Quarterly 47 (2):205-210.score: 21.0
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  24. Arthur W. Apter (2011). Indestructibility, HOD, and the Ground Axiom. Mathematical Logic Quarterly 57 (3):261-265.score: 21.0
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  25. Norbert Brunner, Karl Svozil & Matthias Baaz (1996). The Axiom of Choice in Quantum Theory. Mathematical Logic Quarterly 42 (1):319-340.score: 21.0
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  26. 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: 21.0
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  27. 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: 21.0
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  28. Martin Dowd (1993). Remarks on Levy's Reflection Axiom. Mathematical Logic Quarterly 39 (1):79-95.score: 21.0
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  29. H. Herrlich (2003). The Axiom of Choice Holds Iff Maximal Closed Filters Exist. Mathematical Logic Quarterly 49 (3):323.score: 21.0
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  30. Paul Howard (2007). Bases, Spanning Sets, and the Axiom of Choice. Mathematical Logic Quarterly 53 (3):247-254.score: 21.0
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  31. M. Rathjen (2001). Kripke-Platek Set Theory and the Anti-Foundation Axiom. Mathematical Logic Quarterly 47 (4):435-440.score: 21.0
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  32. 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: 21.0
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  33. J. Brendle (2000). Martin's Axiom and the Dual Distributivity Number. Mathematical Logic Quarterly 46 (2):241-248.score: 21.0
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  34. Norbert Brunner & H. Reiju Mihara (2000). Arrow's Theorem, Weglorz' Models and the Axiom of Choice. Mathematical Logic Quarterly 46 (3):335-359.score: 21.0
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  35. Norbert Brunner & Paul Howard (1992). Russell's Alternative to the Axiom of Choice. Mathematical Logic Quarterly 38 (1):529-534.score: 21.0
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  36. 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: 21.0
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  37. K. Diener (2000). On Kappa-Hereditary Sets and Consequences of the Axiom of Choice. Mathematical Logic Quarterly 46 (4):563-568.score: 21.0
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  38. Juliette Dodu & Marianne Morillon (1999). The Hahn-Banach Property and the Axiom of Choice. Mathematical Logic Quarterly 45 (3):299-314.score: 21.0
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  39. Sandra Fontani, Franco Montagna & Andrea Sorbi (1994). A Note on Relative Efficiency of Axiom Systems. Mathematical Logic Quarterly 40 (2):261-272.score: 21.0
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  40. G. Gutierres (2003). Sequential Topological Conditions in &Unknown; in the Absence of the Axiom of Choice. Mathematical Logic Quarterly 49 (3):293.score: 21.0
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  41. Paul Howard, Kyriakos Keremedis, Herman Rubin & Jean E. Rubin (1998). Versions of Normality and Some Weak Forms of the Axiom of Choice. Mathematical Logic Quarterly 44 (3):367-382.score: 21.0
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  42. Kyriakos Keremedis (1998). Extending Independent Sets to Bases and the Axiom of Choice. Mathematical Logic Quarterly 44 (1):92-98.score: 21.0
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  43. Kyriakos Keremedis (1998). Filters, Antichains and Towers in Topological Spaces and the Axiom of Choice. Mathematical Logic Quarterly 44 (3):359-366.score: 21.0
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  44. K. Keremedis & E. Tachtsis (2001). Some Weak Forms of the Axiom of Choice Restricted to the Real Line. Mathematical Logic Quarterly 47 (3):413-422.score: 21.0
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  45. Kyriakos Keremedis (2003). The Failure of the Axiom of Choice Implies Unrest in the Theory of Lindelöf Metric Spaces. Mathematical Logic Quarterly 49 (2):179-186.score: 21.0
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  46. Victor Pambuccian (2010). Forms of the Pasch Axiom in Ordered Geometry. Mathematical Logic Quarterly 56 (1):29-34.score: 21.0
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  47. Arthur L. Rubin & Jean E. Rubin (1993). Weak Forms of the Axiom of Choice and the Generalized Continuum Hypothesis. Mathematical Logic Quarterly 39 (1):7-22.score: 21.0
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  48. Thilo Weinert (2010). The Bounded Axiom A Forcing Axiom. Mathematical Logic Quarterly 56 (6):659-665.score: 21.0
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  49. 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: 21.0
    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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  50. 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: 21.0
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