29 found
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  1.  22
    Can There Be No Nonrecursive Functions?Joan Rand Moschovakis - 1971 - Journal of Symbolic Logic 36 (2):309-315.
  2.  19
    Intuitionistic Analysis at the End of Time.Joan Rand Moschovakis - 2017 - Bulletin of Symbolic Logic 23 (3):279-295.
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  3.  25
    Classical and Constructive Hierarchies in Extended Intuitionistic Analysis.Joan Rand Moschovakis - 2003 - Journal of Symbolic Logic 68 (3):1015-1043.
    This paper introduces an extension A of Kleene's axiomatization of Brouwer's intuitionistic analysis, in which the classical arithmetical and analytical hierarchies are faithfully represented as hierarchies of the domains of continuity. A domain of continuity is a relation R(α) on Baire space with the property that every constructive partial functional defined on {α : R(α)} is continuous there. The domains of continuity for A coincide with the stable relations (those equivalent in A to their double negations), while every relation R(α) (...)
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  4.  21
    More About Relatively Lawless Sequences.Joan Rand Moschovakis - 1994 - Journal of Symbolic Logic 59 (3):813-829.
    In the author's Relative lawlessness in intuitionistic analysis [this JOURNAL. vol. 52 (1987). pp. 68-88] and An intuitionistic theory of lawlike, choice and lawless sequences [Logic Colloquium '90. Springer-Verlag. Berlin. 1993. pp. 191-209] a notion of lawless ness relative to a countable information base was developed for classical and intuitionistic analysis. Here we simplify the predictability property characterizing relatively lawless sequences and derive it from the new axiom of closed data (classically equivalent to open data) together with a natural principle (...)
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  5.  8
    A Classical View of the Intuitionistic Continuum.Joan Rand Moschovakis - 1996 - Annals of Pure and Applied Logic 81 (1-3):9-24.
  6. Some Axioms for Constructive Analysis.Joan Rand Moschovakis & Garyfallia Vafeiadou - 2012 - Archive for Mathematical Logic 51 (5-6):443-459.
    This note explores the common core of constructive, intuitionistic, recursive and classical analysis from an axiomatic standpoint. In addition to clarifying the relation between Kleene’s and Troelstra’s minimal formal theories of numbers and number-theoretic sequences, we propose some modified choice principles and other function existence axioms which may be of use in reverse constructive analysis. Specifically, we consider the function comprehension principles assumed by the two minimal theories EL and M, introduce an axiom schema CFd asserting that every decidable property (...)
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  7.  34
    Relative Lawlessness in Intuitionistic Analysis.Joan Rand Moschovakis - 1987 - Journal of Symbolic Logic 52 (1):68-88.
    This paper introduces, as an alternative to the (absolutely) lawless sequences of Kreisel and Troelstra, a notion of choice sequence lawless with respect to a given class D of lawlike sequences. For countable D, the class of D-lawless sequences is comeager in the sense of Baire. If a particular well-ordered class F of sequences, generated by iterating definability over the continuum, is countable then the F-lawless, sequences satisfy the axiom of open data and the continuity principle for functions from lawless (...)
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  8.  41
    Luitzen Egbertus Jan Brouwer. On the Significance of the Principle of Excluded Middle in Mathematics, Especially in Function Theory, English Translation of 15516 by Stefan Bauer-Mengelberg and Jean van Heijenoort. From Frege to Gödel, A Source Book in Mathematical Logic, 1879–1931, Edited by Jean van Heijenoort, Harvard University Press, Cambridge, Massachusetts, 1967, Pp. 334–341. Addenda and Corrigenda, English Translation of XXIV 189 by Stefan Bauer-Mengelberg, Claske M. Berndes Franck, Dirk van Dalen, and Jean van Heijenoort. Ibid., Pp. 341–342. Further Addenda and Corrigenda. English Translation of XXIV 189 by Stefan Bauer-Mengelberg, Dirk van Dalen, and Jean van Heijenoort. Ibid., Pp. 342–345. - Luitzen Egbertus Jan Brouwer. On the Domains of Definition of Functions. From Frege to Gödel, A Source Book in Mathematical Logic, 1879–1931, Edited by Jean van Heijenoort, Harvard University Press, Cambridge, Massachusetts, 1967, Pp. 446–463. English Translation of §§1–3 of Über Definiti. [REVIEW]Joan Rand Moschovakis - 1970 - Journal of Symbolic Logic 35 (2):332-333.
  9.  29
    Dieter Rödding. Anzahlquantoren in der Kleene-Hierarchie.Archiv für mathematische Logik und Grundlagenforschung, vol. 9 no. 3–4 , pp. 61–65. [REVIEW]Joan Rand Moschovakis - 1968 - Journal of Symbolic Logic 33 (3):472-473.
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  10.  27
    G. Kreisel. A Remark on Free Choice Sequences and the Topological Completeness Proofs. The Journal of Symbolic Logic, Vol. 23 No. 4 , Pp. 369–388. [REVIEW]Joan Rand Moschovakis - 1967 - Journal of Symbolic Logic 32 (2):283-283.
  11.  26
    L. E. J. Brouwer. On the Foundations of Mathematics. English Translation of 1551, with Added Notes by the Editor. L. E. J. Brouwer, Collected Works, Volume 1, Philosophy and Foundations of Mathematics, Edited by A. Heyting, North-Holland Publishing Company, Amsterdam and Oxford, and American Elsevier Publishing Company, Inc., New York, 1975, Pp. 13–101, 565–569. - L. E. J. Brouwer. Die Möglichen Mächtigkeiten. A Reprint of 1554, with Added Notes by the Editor. L. E. J. Brouwer, Collected Works, Volume 1, Philosophy and Foundations of Mathematics, Edited by A. Heyting, North-Holland Publishing Company, Amsterdam and Oxford, and American Elsevier Publishing Company, Inc., New York, 1975, Pp. 102-104, 569. - L. E. J. Brouwer. On the Foundations of Mathematics. Partial English Translation of 1553, with Added Notes by the Editor. L. E. J. Brouwer, Collected Works, Volume 1, Philosophy and Foundations of Mathematics, Edited by A. Heyting, North-Holland Publishing Company, Amsterdam and Oxfor. [REVIEW]Joan Rand Moschovakis - 1979 - Journal of Symbolic Logic 44 (2):271-275.
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  12.  22
    Dieter Rödding. Anzahlquantoren in der Prädikatenlogik. Archiv für mathematische Logik und Grundlagenforschung, vol. 9 no. 3–4 , pp. 66–69. [REVIEW]Joan Rand Moschovakis - 1968 - Journal of Symbolic Logic 33 (3):473.
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  13.  21
    G. Kreisel. Elementary Completeness Properties of Intuitionistic Logic with a Note on Negations of Prenex Formulae. The Journal of Symbolic Logic, Vol. 23 No. 3 , Pp. 317–330. [REVIEW]Joan Rand Moschovakis - 1967 - Journal of Symbolic Logic 32 (2):282-283.
  14.  7
    In memoriam: Anne sjerp Troelstra 1939–2019.Dick de Jongh & Joan Rand Moschovakis - 2020 - Bulletin of Symbolic Logic 26 (3-4):293-295.
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  15.  17
    L. E. J. Brouwer. Points and Spaces. Canadian Journal of Mathematics, Vol. 6 , Pp. 1–17.Joan Rand Moschovakis - 1969 - Journal of Symbolic Logic 34 (3):519.
  16.  17
    John Myhill. The Formalization of Intuitionism. Contemporary Philosophy, A Survey, I, Logic and Foundations of Mathematics , Edited by Raymond Klibansky, La Nuova Italia Editrice, Florence 1968, Pp. 324–341. [REVIEW]Joan Rand Moschovakis - 1975 - Journal of Symbolic Logic 40 (4):625.
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  17.  15
    G. Kreisel. On Weak Completeness of Intuitionistic Predicate Logic. The Journal of Symbolic Logic, Vol. 27 No. 2 , Pp. 139–158.Joan Rand Moschovakis - 1969 - Journal of Symbolic Logic 34 (1):119-120.
  18.  14
    John Myhill. The invalidity of Markoff's schema. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 9 , pp. 359–360. [REVIEW]Joan Rand Moschovakis - 1974 - Journal of Symbolic Logic 39 (2):333-334.
  19.  12
    Yu. T. Medvedev. Finite Problems. English Translation of XXXVIII 356 by Elliott Mendelson. Soviet Mathematics, Vol. 3 No. 1 , Pp. 227–230. - Yu. T. Medvedev. Interpretation of Logical Formulas by Means of Finite Problems and its Relation to the Readability Theory. English Translation of XXXVIII 356 by Sue Ann Walker. Soviet Mathematics, Vol. 4 No. 1 , Pp. 180–183. - Ju. T. Medvedev. Interpretation of Logical Formulas by Means of Finite Problems. English Translation of XXXVIII 356 by Sue Ann Walker. Soviet Mathematics, Vol. 7 No. 4 , Pp. 857–860. [REVIEW]Joan Rand Moschovakis - 1973 - Journal of Symbolic Logic 38 (2):330-331.
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  20.  19
    A. S. Troelstra. Principles of Intuitionism. Lectures Presented at the Summer Conference on Intuitionism and Proof Theory at SUNY at Buffalo, N. Y. Lecture Notes in Mathematics, No. 95. Springer-Verlag, Berlin, Heidelberg, and New York, 1969, 111 Pp. [REVIEW]Joan Rand Moschovakis - 1975 - Journal of Symbolic Logic 40 (3):447-448.
  21.  15
    Review: M. D. Krol, The Topological Models of Intuitionistic Analysis. One Counterexample; M. D. Krol, A Topological Model for Intuitionistic Analysis with Kripke's Scheme; M. D. Krol', B. F. Wells, Distinct Variants of Kripke's Schema in Intuitionistic Analysis. [REVIEW]Joan Rand Moschovakis - 1981 - Journal of Symbolic Logic 46 (3):660-661.
  22.  18
    Review: L. E. J. Brouwer, L.E.J. Brouwer, Collected Works. [REVIEW]Joan Rand Moschovakis - 1979 - Journal of Symbolic Logic 44 (2):271-275.
  23.  14
    Review: L. E. J. Brouwer, Points and Spaces. [REVIEW]Joan Rand Moschovakis - 1969 - Journal of Symbolic Logic 34 (3):519-519.
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  24.  13
    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]Joan Rand Moschovakis - 1970 - Journal of Symbolic Logic 35 (2):332-333.
  25.  9
    Review: Dieter Rodding, Anzahlquantoren in der Kleene-Hierarchie. [REVIEW]Joan Rand Moschovakis - 1968 - Journal of Symbolic Logic 33 (3):472-473.
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  26.  9
    Review: G. Kreisel, On Weak Completeness of Intuitionistic Predicate Logic. [REVIEW]Joan Rand Moschovakis - 1969 - Journal of Symbolic Logic 34 (1):119-120.
  27.  6
    Review: Dieter Rodding, Anzahlquantoren in der Pradikatenlogik. [REVIEW]Joan Rand Moschovakis - 1968 - Journal of Symbolic Logic 33 (3):473-473.
  28.  4
    Review: John Myhill, Raymond Klibansky, The Formalization of Intuitionism. [REVIEW]Joan Rand Moschovakis - 1975 - Journal of Symbolic Logic 40 (4):625-625.
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  29.  10
    Analyzing Realizability by Troelstra's Methods.Joan Rand Moschovakis - 2002 - Annals of Pure and Applied Logic 114 (1-3):203-225.
    Realizabilities are powerful tools for establishing consistency and independence results for theories based on intuitionistic logic. Troelstra discovered principles ECT 0 and GC 1 which precisely characterize formal number and function realizability for intuitionistic arithmetic and analysis, respectively. Building on Troelstra's results and using his methods, we introduce the notions of Church domain and domain of continuity in order to demonstrate the optimality of “almost negativity” in ECT 0 and GC 1 ; strengthen “double negation shift” DNS 0 to DNS (...)
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