Results for 'Intuitionistic mathematics'

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  1.  3
    Decidability and Specker Sequences in Intuitionistic Mathematics.Mohammad Ardeshir & Rasoul Ramezanian - 2009 - Mathematical Logic Quarterly 55 (6):637-648.
    A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema about intuitionistic decidability that asserts “there exists an (...)
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  2. The Foundations of Intuitionistic Mathematics.Stephen Cole Kleene - 1965 - Amsterdam: North-Holland Pub. Co..
     
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  3.  16
    Choice Sequences: A Chapter of Intuitionistic Mathematics.A. S. Troelstra - 1977 - Clarendon Press.
  4. Intuitionistic Mathematics and Logic.Michael A. E. Dummett - 1974 - Mathematical Institute.
  5. Axioms for Intuitionistic Mathematics Incompatible with Classical Logic.A. S. Troelstra - 1975 - Mathematisch Instituut.
     
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  6.  9
    Reverse Mathematics and Completeness Theorems for Intuitionistic Logic.Takeshi Yamazaki - 2001 - Notre Dame Journal of Formal Logic 42 (3):143-148.
    In this paper, we investigate the logical strength of completeness theorems for intuitionistic logic along the program of reverse mathematics. Among others we show that is equivalent over to the strong completeness theorem for intuitionistic logic: any countable theory of intuitionistic predicate logic can be characterized by a single Kripke model.
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  7.  62
    Intuitionistic Mathematics Does Not Needex Falso Quodlibet.Neil Tennant - 1994 - Topoi 13 (2):127-133.
    We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX. Thus IR establishes the same inconsistencies and theorems as intuitionistic logic, and allows one to prove every intuitionistic (...)
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  8.  48
    Intuitionistic Mathematics and Wittgenstein.Wenceslao J. Gonzalez - 1991 - History and Philosophy of Logic 12 (2):167-183.
    The relation between Wittgenstein's philosophy of mathematics and mathematical Intuitionism has raised a considerable debate. My attempt is to analyse if there is a commitment in Wittgenstein to themes characteristic of the intuitionist movement in Mathematics and if that commitment is one important strain that runs through his Remarks on the foundations of mathematics. The intuitionistic themes to analyse in his philosophy of mathematics are: firstly, his attacks on the unrestricted use of the Law of (...)
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  9.  66
    Temporal and Atemporal Truth in Intuitionistic Mathematics.Enrico Martino & Gabriele Usberti - 1994 - Topoi 13 (2):83-92.
    In section 1 we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of theclassical meaning of the logical constants, and consequently is incompatible with the antirealism of orthodox intuitionism. In section 2 we show how what we call the potential intuitionistic meaning of the logical constants can be defined, on the one hand, by means of the notion of atemporal (...)
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  10.  55
    Hermann Weyl's Intuitionistic Mathematics.Van Dalen Dirk - 1995 - Bulletin of Symbolic Logic 1 (2):145-169.
  11.  15
    The Foundations of Intuitionistic Mathematics[REVIEW]J. M. P. - 1965 - Review of Metaphysics 19 (1):154-155.
  12.  44
    G. F. C. Griss and His Negationless Intuitionistic Mathematics.A. Heyting - 1955 - Synthese 9 (1):91 - 96.
  13.  3
    Recursive Functions and Intuitionistic Mathematics.S. C. Kleene - 1953 - Journal of Symbolic Logic 18 (2):181-182.
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  14. Review: Clifford Spector, Provably Recursive Functionals of Analysis: A Consistency Proof of Analysis by an Extension of Principles Formulated in Current Intuitionistic Mathematics[REVIEW]R. E. Vesley - 1967 - Journal of Symbolic Logic 32 (1):128-128.
     
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  15.  17
    Perspectives on the Dispute Between Intuitionistic and Classical Mathematics.Dag Westerståhl - 2004 - In Christer Svennerlind (ed.), Ursus Philosophicus. Essays dedicated to Björn Haglund on his sixtieth birthday. Philosophical Communications.
    It is not unreasonable to think that the dispute between classical and intuitionistic mathematics might be unresolvable or 'faultless', in the sense of there being no objective way to settle it. If so, we would have a pretty case of relativism. In this note I argue, however, that there is in fact not even disagreement in any interesting sense, let alone a faultless one, in spite of appearances and claims to the contrary. A position I call classical pluralism (...)
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  16.  4
    Semantical Considerations on Intuitionistic Mathematics.E. W. Beth - 1948 - Journal of Symbolic Logic 13 (3):173-173.
  17.  3
    Review: E. W. Beth, Semantical Considerations on Intuitionistic Mathematics[REVIEW]S. C. Kleene - 1948 - Journal of Symbolic Logic 13 (3):173-173.
  18.  7
    Review: A. S. Troelstra, Choice Sequences. A Chapter of Intuitionistic Mathematics[REVIEW]Richard Vesley - 1979 - Journal of Symbolic Logic 44 (2):275-276.
  19. Classical Extensions of Intuitionistic Mathematics.S. C. Kleene - 1965 - In Yehoshua Bar-Hillel (ed.), Logic, Methodology and Philosophy of Science. Amsterdam: North-Holland Pub. Co.. pp. 2--31.
     
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  20.  4
    Review: L. E. J. Brouwer, Directives of Intuitionistic Mathematics[REVIEW]Evert W. Beth - 1947 - Journal of Symbolic Logic 12 (4):136-136.
  21. Beth E. W.. Semantical Considerations on Intuitionistic Mathematics. Koninklijke Nederlandsche Akademie van Wetenschappen, Proceedings of the Section of Sciences, Vol. 50 , Pp. 1246–1251, and Ibid., Pp. 572–577. [REVIEW]S. C. Kleene - 1948 - Journal of Symbolic Logic 13 (3):173.
  22.  3
    Review: A. Heyting, Intuitionistic Mathematics[REVIEW]Evert Beth - 1940 - Journal of Symbolic Logic 5 (2):73-74.
  23.  3
    Review: G. F. C. Griss, Negation-Free Intuitionistic Mathematics[REVIEW]Evert W. Beth - 1946 - Journal of Symbolic Logic 11 (1):24-24.
  24.  3
    Review: J. J. De Iongh, Restricted Forms of Intuitionistic Mathematics[REVIEW]David Nelson - 1949 - Journal of Symbolic Logic 14 (3):183-184.
  25.  2
    Review: A. Heyting, The Development of Intuitionistic Mathematics[REVIEW]Alonzo Church - 1937 - Journal of Symbolic Logic 2 (2):89-89.
  26.  1
    Troelstra A. S.. Choice Sequences. A Chapter of Intuitionistic Mathematics. Oxford Logic Guides. Clarendon Press, Oxford 1977, Ix + 170 Pp. [REVIEW]Richard Vesley - 1979 - Journal of Symbolic Logic 44 (2):275-276.
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  27.  1
    Griss G. F. C.. Negationless Intuitionistic Mathematics II, III, IV. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings of the Section of Sciences, Vol. 53 , Pp. 456–463, and Series A, Vol. 54 , Pp. 193–199, 452–471; Also Indagationes Mathematicae, Vol. 12 , Pp. 108–115, and Vol. 13 , Pp. 193–199, 452–471. [REVIEW]P. G. J. Vredenduin - 1954 - Journal of Symbolic Logic 19 (4):296-297.
  28.  2
    Review: S. C. Kleene, Recursive Functions and Intuitionistic Mathematics[REVIEW]Andrzej Mostowski - 1953 - Journal of Symbolic Logic 18 (2):181-182.
  29.  2
    Review: A. Heyting, G. F. C. Griss and His Negationaless Intuitionistic Mathematics[REVIEW]P. G. J. Vredenduin - 1956 - Journal of Symbolic Logic 21 (1):91-91.
  30.  2
    Review: G. F. C. Griss, Negationless Intuitionistic Mathematics II, III, IV. [REVIEW]P. G. J. Vredenduin - 1954 - Journal of Symbolic Logic 19 (4):296-297.
  31.  1
    Review: G. F. C. Griss, Negationless Intuitionistic Mathematics[REVIEW]Evert W. Beth - 1947 - Journal of Symbolic Logic 12 (2):62-62.
  32.  1
    Logic of Negationless Intuitionistic Mathematics.G. F. C. Griss - 1955 - Journal of Symbolic Logic 20 (1):67-68.
  33.  1
    Negationless Intuitionistic Mathematics.G. F. C. Griss - 1947 - Journal of Symbolic Logic 12 (2):62-62.
  34.  1
    Intuïtionistic Mathematics.A. Heyting - 1940 - Journal of Symbolic Logic 5 (2):73-74.
  35.  1
    The Development of Intuitionistic Mathematics.A. Heyting - 1937 - Journal of Symbolic Logic 2 (2):89-89.
  36.  1
    Choice Sequences: A Chapter of Intuitionistic Mathematics.Mary Tiles - 1978 - Philosophical Books 19 (2):77-80.
  37. Chandrasekharan K.. The Logic of Intuitionistic Mathematics. The Mathematics Student , Vol. 9 No. 4 , Pp. 143–154.Alonzo Church - 1942 - Journal of Symbolic Logic 7 (4):171.
  38. Griss G. F. C.. Negationless Intuitionistic Mathematics. Indagationes Mathematicae, Vol. 8 , Pp. 675–681. [Same as XII 62.]. [REVIEW]Alonzo Church - 1948 - Journal of Symbolic Logic 13 (3):174.
  39. Review: G. F. C. Griss, Negationless Intuitionistic Mathematics; J. Ridder, Ueber den Aussagen-und den Engeren Pradikatenkalkul; L. E. J. Brouwer, Richtlijnen der Intuitionistische Wiskunde. [REVIEW]Alonzo Church - 1948 - Journal of Symbolic Logic 13 (3):174-174.
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  40. Review: K. Chandrasekharan, The Logic of Intuitionistic Mathematics[REVIEW]Alonzo Church - 1942 - Journal of Symbolic Logic 7 (4):171-171.
  41. A.S. TROELSTRA "Choice Sequences. A Chapter of Intuitionistic Mathematics". [REVIEW]R. E. Grandy - 1983 - History and Philosophy of Logic 4 (2):241.
  42. Negationless Intuitionistic Mathematics II, III, IV.G. F. C. Griss - 1954 - Journal of Symbolic Logic 19 (4):296-297.
  43. Negationless Intuitionistic Mathematics.G. F. C. Griss, J. Ridder & L. E. J. Brouwer - 1948 - Journal of Symbolic Logic 13 (3):174-174.
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  44. G. F. C. Griss and His Negationless Intuitionistic Mathematics.A. Heyting - 1953 - Synthese 9 (2):91-96.
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  45. Kleene S. C.. Recursive Functions and Intuitionistic Mathematics. Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30-September 6, 1950, American Mathematical Society, Providence 1952, Vol. I, Pp. 679–685. [REVIEW]Andrzej Mostowski - 1953 - Journal of Symbolic Logic 18 (2):181-182.
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  46. De Iongh J. J.. Restricted Forms of Intuitionistic Mathematics. Actes du Xme Congrès International de Philosophie —Proceedings of the Tenth International Congress of Philosophy , North-Holland Publishing Company, Amsterdam 1949, Pp. 744–748. [REVIEW]David Nelson - 1949 - Journal of Symbolic Logic 14 (3):183-184.
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  47. Spector Clifford. Provably Recursive Functionals of Analysis: A Consistency Proof of Analysis by an Extension of Principles Formulated in Current Intuitionistic Mathematics. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 1–27. [REVIEW]R. E. Vesley - 1967 - Journal of Symbolic Logic 32 (1):128.
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  48. Heyting A.. G. F. C. Griss and His Negationless Intuitionistic Mathematics. Synthese, Vol. 9, Issue 2 No. 2 , Pp. 91–96. [REVIEW]P. G. J. Vredenduin - 1956 - Journal of Symbolic Logic 21 (1):91.
  49. Review: G. F. C. Griss, Logic of Negationless Intuitionistic Mathematics[REVIEW]P. G. J. Vredenduin - 1955 - Journal of Symbolic Logic 20 (1):67-68.
  50.  69
    Intuitionistic Views on the Nature of Mathematics.Arend Heyting - 1974 - Synthese 27 (1-2):79 - 91.
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