Search results for 'Intuitionistic mathematics' (try it on Scholar)

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  1.  2
    Mohammad Ardeshir & Rasoul Ramezanian (2009). Decidability and Specker Sequences in Intuitionistic Mathematics. 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. Stephen Cole Kleene (1965). The Foundations of Intuitionistic Mathematics. Amsterdam, North-Holland Pub. Co..
     
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  3.  7
    A. S. Troelstra (1977). Choice Sequences: A Chapter of Intuitionistic Mathematics. Clarendon Press.
  4. Michael A. E. Dummett (1974). Intuitionistic Mathematics and Logic. Mathematical Institute.
  5. A. S. Troelstra (1975). Axioms for Intuitionistic Mathematics Incompatible with Classical Logic. Mathematisch Instituut.
     
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  6.  7
    Takeshi Yamazaki (2001). Reverse Mathematics and Completeness Theorems for Intuitionistic Logic. 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.  40
    Neil Tennant (1994). Intuitionistic Mathematics Does Not Needex Falso Quodlibet. 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.  41
    Wenceslao J. Gonzalez (1991). Intuitionistic Mathematics and Wittgenstein. 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.  42
    Enrico Martino & Gabriele Usberti (1994). Temporal and Atemporal Truth in Intuitionistic Mathematics. 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.  31
    Dirk Van Dalen (1995). Hermann Weyl's Intuitionistic Mathematics. Bulletin of Symbolic Logic 1 (2):145-169.
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  11.  18
    Dirk Van Dalen (1995). Hermann Weyl's Intuitionistic Mathematics. Bulletin of Symbolic Logic 1 (2):145 - 169.
  12. R. E. Vesley (1967). Review: Clifford Spector, Provably Recursive Functionals of Analysis: A Consistency Proof of Analysis by an Extension of Principles Formulated in Current Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 32 (1):128-128.
     
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  13.  23
    A. Heyting (1955). G. F. C. Griss and His Negationless Intuitionistic Mathematics. Synthese 9 (1):91 - 96.
  14.  13
    Dag Westerståhl (2004). Perspectives on the Dispute Between Intuitionistic and Classical Mathematics. 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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  15.  5
    P. J. M. (1965). The Foundations of Intuitionistic Mathematics. Review of Metaphysics 19 (1):154-155.
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  16.  2
    J. M. P. (1965). The Foundations of Intuitionistic Mathematics. [REVIEW] Review of Metaphysics 19 (1):154-155.
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  17.  1
    E. W. Beth (1948). Semantical Considerations on Intuitionistic Mathematics. Journal of Symbolic Logic 13 (3):173-173.
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  18.  2
    S. C. Kleene (1948). Review: E. W. Beth, Semantical Considerations on Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 13 (3):173-173.
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  19.  4
    Richard Vesley (1979). Review: A. S. Troelstra, Choice Sequences. A Chapter of Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 44 (2):275-276.
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  20.  3
    David Nelson (1949). Review: J. J. De Iongh, Restricted Forms of Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 14 (3):183-184.
  21.  1
    A. Heyting (1940). Intuïtionistic Mathematics. Journal of Symbolic Logic 5 (2):73-74.
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  22.  1
    A. Heyting (1937). The Development of Intuitionistic Mathematics. Journal of Symbolic Logic 2 (2):89-89.
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  23. S. C. Kleene (1965). Classical Extensions of Intuitionistic Mathematics. In Yehoshua Bar-Hillel (ed.), Logic, Methodology and Philosophy of Science. Amsterdam, North-Holland Pub. Co. 2--31.
     
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  24.  1
    Alonzo Church (1937). Review: A. Heyting, The Development of Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 2 (2):89-89.
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  25.  2
    P. G. J. Vredenduin (1956). Review: A. Heyting, G. F. C. Griss and His Negationaless Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 21 (1):91-91.
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  26.  2
    Evert W. Beth (1947). Review: L. E. J. Brouwer, Directives of Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 12 (4):136-136.
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  27.  2
    P. G. J. Vredenduin (1954). Review: G. F. C. Griss, Negationless Intuitionistic Mathematics II, III, IV. [REVIEW] Journal of Symbolic Logic 19 (4):296-297.
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  28.  1
    Evert Beth (1940). Review: A. Heyting, Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 5 (2):73-74.
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  29.  1
    Andrzej Mostowski (1953). Review: S. C. Kleene, Recursive Functions and Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 18 (2):181-182.
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  30.  1
    Evert W. Beth (1946). Review: G. F. C. Griss, Negation-Free Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 11 (1):24-24.
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  31. Evert W. Beth (1947). Review: G. F. C. Griss, Negationless Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 12 (2):62-62.
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  32. Alonzo Church (1948). 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] Journal of Symbolic Logic 13 (3):174-174.
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  33. Alonzo Church (1942). Review: K. Chandrasekharan, The Logic of Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 7 (4):171-171.
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  34. R. E. Grandy (1983). A.S. TROELSTRA "Choice Sequences. A Chapter of Intuitionistic Mathematics". [REVIEW] History and Philosophy of Logic 4 (2):241.
     
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  35. G. F. C. Griss (1955). Logic of Negationless Intuitionistic Mathematics. Journal of Symbolic Logic 20 (1):67-68.
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  36. G. F. C. Griss (1947). Negationless Intuitionistic Mathematics. Journal of Symbolic Logic 12 (2):62-62.
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  37. G. F. C. Griss (1954). Negationless Intuitionistic Mathematics II, III, IV. Journal of Symbolic Logic 19 (4):296-297.
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  38. Mary Tiles (1978). Choice Sequences: A Chapter of Intuitionistic Mathematics. Philosophical Books 19 (2):77-80.
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  39. P. G. J. Vredenduin (1955). Review: G. F. C. Griss, Logic of Negationless Intuitionistic Mathematics. [REVIEW] Journal of Symbolic Logic 20 (1):67-68.
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  40.  44
    Arend Heyting (1974). Intuitionistic Views on the Nature of Mathematics. Synthese 27 (1-2):79 - 91.
  41.  2
    Kentaro Sato (2015). A New Model Construction by Making a Detour Via Intuitionistic Theories II: Interpretability Lower Bound of Feferman's Explicit Mathematics T 0. Annals of Pure and Applied Logic 166 (7-8):800-835.
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  42.  9
    Daniel Vanderveken (1991). J. Couture and J. Lambek,'Philosophical Reflections on the Foun-Dations of Mathematics', Erkenntnis 34 (1991) 187-209. In the Statement of “Giidel's Formula G is False in the Free Topos” on Page 201, Line 16 Fb, the Word “False” Should Be Replaced by “Not True”.(As the Internal Language of the Free Topos is Intuitionistic, This). [REVIEW] Erkenntnis 34:187-209.
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  43.  3
    Marek Zawadowski (1995). Pitts Andrew M.. Interpolation and Conceptual Completeness for Pretoposes Via Category Theory. Mathematical Logic and Theoretical Computer Science, Edited by David W. Kueker, Edgar GK Lopez-Escobar and Carl H. Smith, Lecture Notes in Pure and Applied Mathematics, Vol. 106, Marcel Dekker, New York and Basel 1987, Pp. 301–327. Pitts Andrew M.. Conceptual Completeness for First-Order Intuitionistic Logic: An Application of Categorical Logic. Annals of Pure and Applied Logic, Vol. 41 (1989), Pp. 33–81. [REVIEW] Journal of Symbolic Logic 60 (2):692-694.
  44.  13
    Victor N. Krivtsov (2000). A Negationless Interpretation of Intuitionistic Theories. Erkenntnis 53 (1-2):155-179.
    In a seriesof papers beginning in 1944, the Dutch mathematician and philosopherGeorge Francois Cornelis Griss proposed that constructivemathematics should be developedwithout the use of the intuitionistic negation1 and,moreover, without any use of a nullpredicate.In the present work, we give formalized versions of intuitionisticarithmetic, analysis,and higher-order arithmetic in the spirit ofGriss' ``negationless intuitionistic mathematics''and then consider their relation to thecurrent formalizations of thesetheories.
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  45.  14
    Victor N. Krivtsov (2000). A Negationless Interpretation of Intuitionistic Theories. I. Erkenntnis 64 (1-2):323-344.
    In a seriesof papers beginning in 1944, the Dutch mathematician and philosopherGeorge Francois Cornelis Griss proposed that constructivemathematics should be developedwithout the use of the intuitionistic negation1 and,moreover, without any use of a nullpredicate.In the present work, we give formalized versions of intuitionisticarithmetic, analysis,and higher-order arithmetic in the spirit ofGriss' ``negationless intuitionistic mathematics''and then consider their relation to thecurrent formalizations of thesetheories.
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  46.  2
    James R. Geiser (1975). Review: A. S. Yessenin-Volpin, The Ultra-Intuitionistic Criticism and the Antitraditional Program for Foundations of Mathematics. [REVIEW] Journal of Symbolic Logic 40 (1):95-97.
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  47.  2
    Th Skolem (1948). Review: D. Van Dantzig, On the Principles of Intuitionistic and Affirmative Mathematics. [REVIEW] Journal of Symbolic Logic 13 (3):173-173.
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  48.  2
    Joan Rand Moschovakis (1970). Review: Luitzen Egbertus Jan Brouwer, Stefan Bauer-Mangelberg, Jean van Heijenoort, On the Significance of the Principle of Excluded Middle in Mathematics, Especially in Function Theory; Luitzen Egbertus Jan Brouwer, Stefan Bauer-Mengelberg, On the Domains of Definition of Functions; Luitzen Egbertus Jan Brouwer, Stefan Bauer-Mangelberg, Intuitionistic Reflections on Formalism. [REVIEW] Journal of Symbolic Logic 35 (2):332-333.
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  49. Michael A. E. Dummett (2000). Elements of Intuitionism. Oxford University Press.
    This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order (...)
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  50.  79
    Richard L. Tieszen (2005). Phenomenology, Logic, and the Philosophy of Mathematics. Cambridge University Press.
    Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this book is divided into three parts. Part I, Reason, Science, and Mathematics contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay oN phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some (...)
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