Search results for 'Continuum Hypothesis' (try it on Scholar)

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  1. 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: 150.0
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  2. Paul J. Cohen (1966). Set Theory and the Continuum Hypothesis. New York, W. A. Benjamin.score: 150.0
  3. David J. Chalmers, Is the Continuum Hypothesis True, False, or Neither?score: 120.0
    Thanks to all the people who responded to my enquiry about the status of the Continuum Hypothesis. This is a really fascinating subject, which I could waste far too much time on. The following is a summary of some aspects of the feeling I got for the problems. This will be old hat to set theorists, and no doubt there are a couple of embarrassing misunderstandings, but it might be of some interest to non professionals.
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  4. Solomon Feferman, Is the Continuum Hypothesis a Definite Mathematical Problem?score: 120.0
    The purpose of this article is to explain why I believe that the Continuum Hypothesis (CH) is not a definite mathematical problem. My reason for that is that the concept of arbitrary set essential to its formulation is vague or underdetermined and there is no way to sharpen it without violating what it is supposed to be about. In addition, there is considerable circumstantial evidence to support the view that CH is not definite.
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  5. Jaakko Hintikka, Continuum Hypothesis as a Model-Theoretical Problem.score: 120.0
    Jaakko Hintikka 1. How to Study Set Theory The continuum hypothesis (CH) is crucial in the core area of set theory, viz. in the theory of the hierarchies of infinite cardinal and infinite ordinal numbers. It is crucial in that it would, if true, help to relate the two hierarchies to each other. It says that the second infinite cardinal number, which is known to be the cardinality of the first uncountable ordinal, equals the cardinality 2 o of (...)
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  6. Thomas Weston (1976). Kreisel, the Continuum Hypothesis and Second Order Set Theory. Journal of Philosophical Logic 5 (2):281 - 298.score: 120.0
    The major point of contention among the philosophers and mathematicians who have written about the independence results for the continuum hypothesis (CH) and related questions in set theory has been the question of whether these results give reason to doubt that the independent statements have definite truth values. This paper concerns the views of G. Kreisel, who gives arguments based on second order logic that the CH does have a truth value. The view defended here is that although (...)
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  7. Gregory H. Moore (2011). Early History of the Generalized Continuum Hypothesis: 1878—1938. Bulletin of Symbolic Logic 17 (4):489-532.score: 120.0
    This paper explores how the Generalized Continuum Hypothesis (GCH) arose from Cantor's Continuum Hypothesis in the work of Peirce, Jourdain, Hausdorff, Tarski, and how GCH was used up to Gödel's relative consistency result.
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  8. George C. Nelson (1998). Preservation Theorems Without Continuum Hypothesis. Studia Logica 60 (3):343-355.score: 120.0
    Many results concerning the equivalence between a syntactic form of formulas and a model theoretic conditions are proven directly without using any form of a continuum hypothesis. In particular, it is demonstrated that any reduced product sentence is equivalent to a Horn sentence. Moreover, in any first order language without equality one now has that a reduced product sentence is equivalent to a Horn sentence and any sentence is equivalent to a Boolean combination of Horn sentences.
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  9. Ramez L. Sami (1989). Turing Determinacy and the Continuum Hypothesis. Archive for Mathematical Logic 28 (3):149-154.score: 120.0
    From the hypothesis that all Turing closed games are determined we prove: (1) the Continuum Hypothesis and (2) every subset of ℵ1 is constructible from a real.
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  10. Joseph Glicksohn (2004). Absorption, Hallucinations, and the Continuum Hypothesis. Behavioral and Brain Sciences 27 (6):793-794.score: 96.0
    The target article, in stressing the balance between neurobiological and psychological factors, makes a compelling argument in support of a continuum of perceptual and hallucinatory experience. Nevertheless, two points need to be addressed. First, the authors are probably underestimating the incidence of hallucinations in the normal population. Second, one should consider the role of absorption as a predisposing factor for hallucinations.
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  11. Justin Clarke-Doane (2013). What is Absolute Undecidability?†. Noûs 47 (3):467-481.score: 90.0
    It is often alleged that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if (...)
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  12. Uri Abraham (1983). On Forcing Without the Continuum Hypothesis. Journal of Symbolic Logic 48 (3):658-661.score: 90.0
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  13. Joel I. Friedman (1971). The Generalized Continuum Hypothesis is Equivalent to the Generalized Maximization Principle. Journal of Symbolic Logic 36 (1):39-54.score: 90.0
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  14. Richard A. Platek (1969). Eliminating the Continuum Hypothesis. Journal of Symbolic Logic 34 (2):219-225.score: 90.0
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  15. W. Gielen, H. de Swart & W. Veldman (1981). The Continuum Hypothesis in Intuitionism. Journal of Symbolic Logic 46 (1):121-136.score: 90.0
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  16. Thomas S. Weston (1977). The Continuum Hypothesis is Independent of Second-Order ZF. Notre Dame Journal of Formal Logic 18 (3):499-503.score: 90.0
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  17. John Gregory (1976). Higher Souslin Trees and the Generalized Continuum Hypothesis. Journal of Symbolic Logic 41 (3):663-671.score: 90.0
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  18. Rolf Schock (1977). A Note on the Axiom of Choice and the Continuum Hypothesis. Notre Dame Journal of Formal Logic 18 (3):409-414.score: 90.0
  19. Dale Jacquette (1993). A Dialogue on Zeno's Paradox of Achilles and the Tortoise. Argumentation 7 (3):273-290.score: 90.0
    The five participants in this dialogue critically discuss Zeno of Elea's paradox of Achilles and the tortoise. They consider a number of solutions to and restatements of the paradox, together with their philosophical implications. Among the issues investigated include the appearance-reality distinction, Aristotle's distinction between actual and potential infinity, the concept of a continuum, Cantor's continuum hypothesis and theory of transfinite ordinals, and, as a solution to Zeno's puzzle, the distinction between infinite and indeterminate or inexhaustible divisibility.
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  20. Raouf Doss (1963). On Gödel's Proof That $V=L$ Implies the Generalized Continuum Hypothesis. Notre Dame Journal of Formal Logic 4 (4):283-287.score: 90.0
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  21. Paul Cohen (1964). The Independence of the Continuum Hypothesis II. Proc. Nat. Acad. Sci. USA 51 (1):105-110.score: 90.0
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  22. Rolf Schock (1966). A Simple Version of the Generalized Continuum Hypothesis. Notre Dame Journal of Formal Logic 7 (3):287-288.score: 90.0
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  23. Bolesław Sobociński (1962). A Note on the Generalized Continuum Hypothesis. I. Notre Dame Journal of Formal Logic 3 (4):274-278.score: 90.0
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  24. Paul Cohen (1963). The Independence of the Continuum Hypothesis. Proc. Nat. Acad. Sci. USA 50 (6):1143-1148.score: 90.0
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  25. Bolesław Sobociński (1963). A Note on the Generalized Continuum Hypothesis. III. Notre Dame Journal of Formal Logic 4 (3):233-240.score: 90.0
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  26. Bolesław Sobociński (1963). A Note on the Generalized Continuum Hypothesis. II. Notre Dame Journal of Formal Logic 4 (1):67-79.score: 90.0
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  27. W. Gielen, H. De Swart & W. Veldman (1981). The Continuum Hypothesis in Intuitionism. Journal of Symbolic Logic 46 (1):121 - 136.score: 90.0
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  28. Alexander Abian (1973). The Consistency of the Continuum Hypothesis Via Synergistic Models. Mathematical Logic Quarterly 19 (13):193-198.score: 90.0
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  29. M. Boffa (1973). Review: K. Prikry, The Consistency of the Continuum Hypothesis for the First Measurable Cardinal. [REVIEW] Journal of Symbolic Logic 38 (4):652-652.score: 90.0
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  30. F. R. Drake (1973). Review: L. Rieger, On the Consistency of the Generalized Continuum Hypothesis. [REVIEW] Journal of Symbolic Logic 38 (1):153-153.score: 90.0
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  31. Ksenija Maravic da Silva (2013). 6 The Neuropsychology of Visual Hallucinations in Parkinson's Disease and the Continuum Hypothesis. In Fiona Macpherson & Dimitris Platchias (eds.), Hallucination. Mit Press.score: 90.0
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  32. Roy O. Davies (1962). Equivalence to the Continuum Hypothesis of a Certain Proposition of Elementary Plane Geometry. Mathematical Logic Quarterly 8 (2):109-111.score: 90.0
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  33. Keith J. Devlin (1980). Concerning the Consistency of the Souslin Hypothesis with the Continuum Hypothesis. Annals of Mathematical Logic 19 (1-2):115-125.score: 90.0
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  34. William B. Easton (1965). Review: Paul J. Cohen, The Independence of the Continuum Hypothesis. [REVIEW] Journal of Symbolic Logic 30 (3):398-399.score: 90.0
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  35. Ilijas Farah, Paul McKenney & Ernest Schimmerling (2013). Some Calkin Algebras Have Outer Automorphisms. Archive for Mathematical Logic 52 (5-6):517-524.score: 90.0
    We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, assuming some restriction of the Generalized Continuum Hypothesis, there are many outer automorphisms.
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  36. Stephen H. Hechler (1973). Powers of Singular Cardinals and a Strong Form of The Negation of The Generalized Continuum Hypothesis. Mathematical Logic Quarterly 19 (3‐6):83-84.score: 90.0
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  37. Leon Henkin (1952). Review: Kurt Godel, The Consistency of the Axiom of Choice and the Generalized Continuum-Hypothesis with the Axioms of Set Theory. [REVIEW] Journal of Symbolic Logic 17 (3):207-208.score: 90.0
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  38. H. P. K. (1967). Set Theory and the Continuum Hypothesis. Review of Metaphysics 20 (4):716-716.score: 90.0
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  39. J. W. Robbin (1968). Review: Dana Scott, A Proof of the Independence of the Continuum Hypothesis. [REVIEW] Journal of Symbolic Logic 33 (2):293-293.score: 90.0
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  40. Rolf Schock (1971). On the Axiom of Choice and the Continuum Hypothesis. Mathematical Logic Quarterly 17 (1):35-37.score: 90.0
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  41. Boleslaw Sobocinski (1963). A Note On The Generalized Continuum Hypothesis, Ii. Notre Dame Journal of Formal Logic 4 (1):67-79.score: 90.0
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  42. Frederick Bagemihl (1961). A Proposition of Elementary Plane Geometry That Implies the Continuum Hypothesis. Zeitschrift für Mathematische Logik Und Grundlagen der Mathematik 7 (1-5):77-79.score: 90.0
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  43. Frederick Bagemihl (1959). Some Results Connected with the Continuum Hypothesis. Mathematical Logic Quarterly 5 (7‐13):97-116.score: 90.0
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  44. F. Bagemihl & S. Koo (1967). The Continuum Hypothesis and Ambiguous Points of Planar Functions. Zeitschrift für Mathematische Logik Und Grundlagen der Mathematik 13 (13-14):219-223.score: 90.0
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  45. Paul Bernays (1940). Review: Kurt Godel, The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis. [REVIEW] Journal of Symbolic Logic 5 (3):116-117.score: 90.0
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  46. Paul Bernays (1940). Review: Kurt Godel, Consistency-Proof for the Generalized Continuum-Hypothesis. [REVIEW] Journal of Symbolic Logic 5 (3):117-118.score: 90.0
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  47. Paul Bernays (1941). Review: Kurt Godel, George W. Brown, The Consistency of the Axiom of Choice and of the Generalized Continuum- Hypothesis with the Axioms of Set Theory. [REVIEW] Journal of Symbolic Logic 6 (3):112-114.score: 90.0
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  48. U. Blau (1998). A Platonic Argument for Cantor's Continuum Hypothesis (Sets). Dialectica 52 (3):175-202.score: 90.0
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  49. Paul J. Cohen (1963). The Independence of the Continuum Hypothesis. Proceedings of the National Academy of Sciences of the United States of America 50 (6):1143--8.score: 90.0
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  50. F. R. Drake (1969). Review: A. Levy, R. M. Solovay, Measurable Cardinals and the Continuum Hypothesis. [REVIEW] Journal of Symbolic Logic 34 (4):654-655.score: 90.0
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