20 found
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  1.  74
    An Intuitiomstic Completeness Theorem for Intuitionistic Predicate Logic.Wim Veldman - 1976 - Journal of Symbolic Logic 41 (1):159-166.
  2.  36
    Brouwer’s Fan Theorem as an Axiom and as a Contrast to Kleene’s Alternative.Wim Veldman - 2014 - Archive for Mathematical Logic 53 (5-6):621-693.
    The paper is a contribution to intuitionistic reverse mathematics. We introduce a formal system called Basic Intuitionistic MathematicsBIM, and then search for statements that are, over BIM, equivalent to Brouwer’s Fan Theorem or to its positive denial, Kleene’s Alternative to the Fan Theorem. The Fan Theorem is true under the intended intuitionistic interpretation and Kleene’s Alternative is true in the model of BIM consisting of the Turing-computable functions. The task of finding equivalents of Kleene’s Alternative is, intuitionistically, a nontrivial extension (...)
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  3.  22
    Two Simple Sets That Are Not Positively Borel.Wim Veldman - 2005 - Annals of Pure and Applied Logic 135 (1-3):151-209.
    The author proved in his Ph.D. Thesis [W. Veldman, Investigations in intuitionistic hierarchy theory, Ph.D. Thesis, Katholieke Universiteit Nijmegen, 1981] that, in intuitionistic analysis, the positively Borel subsets of Baire space form a genuinely growing hierarchy: every level of the hierarchy contains sets that do not occur at any lower level. It follows from this result that there are natural examples of analytic and also of co-analytic sets that are not positively Borel. It turns out, however, that, in intuitionistic analysis, (...)
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  4.  23
    An Intuitionistic Proof of Kruskal’s Theorem.Wim Veldman - 2004 - Archive for Mathematical Logic 43 (2):215-264.
  5.  6
    Brouwer’s Real Thesis on Bars.Wim Veldman - 2006 - Philosophia Scientae:21-42.
  6.  16
    Some Observations on Intuitionistically Elementary Properties of Linear Orderings.Wim Veldman & Michaël Janssen - 1990 - Archive for Mathematical Logic 29 (3):171-185.
  7.  5
    Brouwer’s Real Thesis on Bars.Wim Veldman - 2006 - Philosophia Scientiae:21-42.
  8.  17
    The Borel Hierarchy Theorem From Brouwer's Intuitionistic Perspective.Wim Veldman - 2008 - Journal of Symbolic Logic 73 (1):1-64.
    In intuitionistic analysis, "Brouwer's Continuity Principle" implies, together with an "Axiom of Countable Choice", that the positively Borel sets form a genuinely growing hierarchy: every level of the hierarchy contains sets that do not occur at any lower level.
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  9.  27
    Enrico Martino.*Intuitionistic Proof Versus Classical Truth, The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics.Wim Veldman - 2019 - Philosophia Mathematica 27 (3):445-450.
    MartinoEnrico.* * Intuitionistic Proof Versus Classical Truth, The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics. Logic, Methodology and the Unity of Science; 42. Springer, 2018. ISBN: 978-3-319-74356-1 ; 978-3-030-08971-9, 978-3-319-74357-8. Pp. xiii + 170.
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  10.  56
    The Fine Structure of the Intuitionistic Borel Hierarchy.Wim Veldman - 2009 - Review of Symbolic Logic 2 (1):30-101.
    In intuitionistic analysis, a subset of a Polish space like or is called positively Borel if and only if it is an open subset of the space or a closed subset of the space or the result of forming either the countable union or the countable intersection of an infinite sequence of (earlier constructed) positively Borel subsets of the space. The operation of taking the complement is absent from this inductive definition, and, in fact, the complement of a positively Borel (...)
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  11.  19
    Martin-Löf Per. An Intuitionistic Theory of Types: Predicative Part. Logic Colloquium '73, Proceedings of the Logic Colloquium, Bristol, July 1973, Edited by Rose H. E. And Shepherdson J. C., Studies in Logic and the Foundations of Mathematics, Vol. 80, North-Holland Publishing Company, Amsterdam and Oxford, and American Elsevier Publishing Company, New York, 1975, Pp. 73–118. [REVIEW]Wim Veldman - 1984 - Journal of Symbolic Logic 49 (1):311-313.
  12.  13
    Aczel Peter. The Type Theoretic Interpretation of Constructive Set Theory. Logic Colloquium '77, Proceedings of the Colloquium Held in Wrocław, August 1977, Edited by Macintyre Angus, Pacholski Leszek, and Paris Jeff, Studies in Logic and the Foundations of Mathematics, Vol. 96, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1978, Pp. 55–66. [REVIEW]Wim Veldman - 1984 - Journal of Symbolic Logic 49 (1):313-314.
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  13.  17
    Review: Per Martin-Lof, H. E. Rose, J. C. Shepherdson, An Intuitionistic Theory of Types: Predicative Part. [REVIEW]Wim Veldman - 1984 - Journal of Symbolic Logic 49 (1):311-313.
  14.  12
    Review: Dov M. Gabbay, Semantical Investigations in Heyting's Intuitionistic Logic. [REVIEW]Wim Veldman - 1986 - Journal of Symbolic Logic 51 (3):824-824.
  15.  8
    Aczel Peter. The Strength of Martin-Löf's Intuitionistic Type Theory with One Universe. Proceedings of the Symposiums on Mathematical Logic in Oulu 1974 and in Helsinki 1975, Edited by Miettinen Seppo and Väänänen Jouko, The Department of Philosophy, University of Helsinki, Helsinki 1977, Pp. 1–32. [REVIEW]Wim Veldman - 1984 - Journal of Symbolic Logic 49 (1):313.
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  16.  8
    Review: Peter Aczel, Angus Macintyre, Leszek Pacholski, Jeff Paris, The Type Theoretic Interpretation of Constructive Set Theory. [REVIEW]Wim Veldman - 1984 - Journal of Symbolic Logic 49 (1):313-314.
  17.  9
    Review: Peter Aczel, Seppo Miettinen, Jouko Vaananen, The Strength of Martin-Lof's Intuitionistic Type Theory with One Universe. [REVIEW]Wim Veldman - 1984 - Journal of Symbolic Logic 49 (1):313-313.
  18.  5
    The Problem of Determinacy of Infinite Games From an Intuitionistic Point of View.Wim Veldman - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag. pp. 351--370.
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  19.  6
    Gabbay Dov M.. Semantical Investigations in Heyting's Intuitionistic Logic. Synthese Library, Vol. 148. D. Reidel Publishing Company, Dordrecht, Boston, and London, 1981, X + 287 Pp. [REVIEW]Wim Veldman - 1986 - Journal of Symbolic Logic 51 (3):824-824.
  20.  16
    Some Elementary Results in Intutionistic Model Theory.Wim Veldman & Frank Waaldijk - 1996 - Journal of Symbolic Logic 61 (3):745-767.
    We establish constructive refinements of several well-known theorems in elementary model theory. The additive group of the real numbers may be embedded elementarily into the additive group of pairs of real numbers, constructively as well as classically.
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