Results for 'S. Troelstra'

941 found
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  1.  72
    Metamathematical investigation of intuitionistic arithmetic and analysis.Anne S. Troelstra - 1973 - New York,: Springer.
  2.  62
    Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.
    The present volume is intended as an all-round introduction to constructivism. Here constructivism is to be understood in the wide sense, and covers in particular Brouwer's intuitionism, Bishop's constructivism and A.A. Markov's constructive recursive mathematics. The ending "-ism" has ideological overtones: "constructive mathematics is the (only) right mathematics"; we hasten, however, to declare that we do not subscribe to this ideology, and that we do not intend to present our material on such a basis.
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  3.  64
    In Memoriam: Albert G. Dragalin 1941–1998.S. Artemov, B. Kushner, G. Mints, E. Nogina & A. Troelstra - 1999 - Bulletin of Symbolic Logic 5 (3):389-391.
  4. (1 other version)Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
     
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  5.  42
    Strong normalization for typed terms with surjective pairing.A. S. Troelstra - 1986 - Notre Dame Journal of Formal Logic 27 (4):547-550.
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  6.  61
    Note on the Fan theorem.A. S. Troelstra - 1974 - Journal of Symbolic Logic 39 (3):584-596.
  7.  71
    Analysing choice sequences.A. S. Troelstra - 1983 - Journal of Philosophical Logic 12 (2):197 - 260.
  8.  42
    Realizability.A. S. Troelstra - 2000 - Bulletin of Symbolic Logic 6 (4):470-471.
  9.  69
    On a second order propositional operator in intuitionistic logic.A. S. Troelstra - 1981 - Studia Logica 40 (2):113 - 139.
    This paper studies, by way of an example, the intuitionistic propositional connective * defined in the language of second order propositional logic by. In full topological models * is not generally definable, but over Cantor-space and the reals it can be classically shown that; on the other hand, this is false constructively, i.e. a contradiction with Church's thesis is obtained. This is comparable with some well-known results on the completeness of intuitionistic first-order predicate logic.Over [0, 1], the operator * is (...)
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  10.  39
    Natural deduction for intuitionistic linear logic.A. S. Troelstra - 1995 - Annals of Pure and Applied Logic 73 (1):79-108.
    The paper deals with two versions of the fragment with unit, tensor, linear implication and storage operator of intuitionistic linear logic. The first version, ILL, appears in a paper by Benton, Bierman, Hyland and de Paiva; the second one, ILL+, is described in this paper. ILL has a contraction rule and an introduction rule !I for the exponential; in ILL+, instead of a contraction rule, multiple occurrences of labels for assumptions are permitted under certain conditions; moreover, there is a different (...)
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  11.  94
    Proof theory and constructive mathematics.Anne S. Troelstra - 1977 - In Jon Barwise, Handbook of mathematical logic. New York: North-Holland. pp. 973--1052.
  12. The Discovery of E.W. Beth’s Semantics for Intuitionistic Logic.A. S. Troelstra & P. van Ulsen - 1999 - In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema, Essays dedicated to Johan van Benthem on the occasion of his 50th birthday. Amsterdam University Press.
     
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  13.  72
    Choice sequences and informal rigour.A. S. Troelstra - 1985 - Synthese 62 (2):217 - 227.
    In this paper we discuss a particular example of the passage from the informal, but rigorous description of a concept to the axiomatic formulation of principles holding for the concept; in particular, we look at the principles of continuity and lawlike choice in the theory of lawless sequences. Our discussion also leads to a better understanding of the rôle of the so-called density axiom for lawless sequences.
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  14.  44
    Informal theory of choice sequences.A. S. Troelstra - 1969 - Studia Logica 25 (1):31 - 54.
  15.  15
    The Theory of Choice Sequences.A. S. Troelstra, B. van Rootselaar & J. F. Staal - 1973 - Journal of Symbolic Logic 38 (2):332-332.
  16. Some models for intuitionistic finite type arithmetic with Fan functional.A. S. Troelstra - 1977 - Journal of Symbolic Logic 42 (2):194-202.
    In this note we shall assume acquaintance with [T4] and the parts of [T1] which deal with intuitionistic arithmetic in all finite types. The bibliography just continues the bibliography of [T4].The principal purpose of this note is the discussion of two models for intuitionistic finite type arithmetic with fan functional. The first model is needed to correct an oversight in the proof of Theorem 6 [T4, §5]: the model ECF+as defined there cannot be shown to have the required properties inEL+ (...)
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  17.  27
    Toshio Umezawa. On logics intermediate between intuitionistic and classical predicate logic. The journal of symbolic logic, vol. 24 no. 2 , pp. 141–153.A. S. Troelstra - 1969 - Journal of Symbolic Logic 33 (4):607.
  18. Construction in Mathematics. An Introduction, Volume 1.A. S. Troelstra & D. van Dalen - 1990 - Studia Logica 49 (1):151-152.
  19.  31
    An addendum.A. S. Troelstra - 1971 - Annals of Mathematical Logic 3 (4):437.
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  20. History of Constructivism in the 20th Century Vol. Ml-91-05.A. S. Troelstra - 1991 - University of Amsterdam.
  21.  52
    Marginalia on sequent calculi.A. S. Troelstra - 1999 - Studia Logica 62 (2):291-303.
    The paper discusses the relationship between normal natural deductions and cutfree proofs in Gentzen (sequent) calculi in the absence of term labeling. For Gentzen calculi this is the usual version; for natural deduction this is the version under the complete discharge convention, where open assumptions are always discharged as soon as possible. The paper supplements work by Mints, Pinto, Dyckhoff, and Schwichtenberg on the labeled calculi.
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  22.  43
    Nieformalna teoria ciągów Z wyboru.A. S. Troelstra - 1969 - Studia Logica 25 (1):53-53.
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  23.  56
    Concepts and Axioms.A. S. Troelstra - 1998 - Philosophia Mathematica 6 (2):195-208.
    The paper discusses the transition from informal concepts to mathematically precise notions; examples are given, and in some detail the case of lawless sequences, a concept of intuitionistic mathematics, is discussed. A final section comments on philosophical discussions concerning intuitionistic logic in connection with a ‘theory of meaning’.
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  24. Constructivism in Mathematics, Volume 2.A. S. Troelstra & D. van Dalen - 1991 - Studia Logica 50 (2):355-356.
  25.  14
    Review: Toshio Umezawa, On Logics Intermediate Between Intuitionistic and Classical Predicate Logic. [REVIEW]A. S. Troelstra - 1968 - Journal of Symbolic Logic 33 (4):607-607.
  26.  20
    The L.E.J. Brouwer Centenary Symposium: proceedings of the conference held in Noordwijkerhout, 8-13 June 1981.L. E. J. Brouwer, A. S. Troelstra & D. van Dalen (eds.) - 1982 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co..
  27. Projections of lawless sequences.D. Van Dalen & A. S. Troelstra - 1970 - In A. Kino, John Myhill & Richard Eugene Vesley, Intuitionism and proof theory. Amsterdam,: North-Holland Pub. Co..
  28.  92
    Realizability and intuitionistic logic.J. Diller & A. S. Troelstra - 1984 - Synthese 60 (2):253 - 282.
  29.  46
    Mariko Yasugi. Intuitionistic analysis and Gödel's interpretation. Journal of the Mathematical Society of Japan, vol. 15 , pp. 101–112. [REVIEW]A. S. Troelstra - 1972 - Journal of Symbolic Logic 37 (2):404.
  30.  54
    Review: A. G. Dragalin, E. Mendelson, Mathematical Intuitionism. Introduction to Proof Theory. [REVIEW]A. S. Troelstra - 1990 - Journal of Symbolic Logic 55 (3):1308-1309.
  31.  33
    Nagashima Takashi. An extension of the Craig-Schütte interpolation theorem. Annals of the Japan Association for Philosophy of Science, vol. 3 no. 1 , pp. 12–18. [REVIEW]A. S. Troelstra - 1968 - Journal of Symbolic Logic 33 (2):291-292.
  32.  28
    (1 other version)Review: Bruno Scarpellini, Proof Theory and Intuitionistic Systems. [REVIEW]A. S. Troelstra - 1974 - Journal of Symbolic Logic 39 (3):607-609.
  33.  54
    Tsutomu Hosoi. On intermediate logics. Journal of the Faculty of Science, University of Tokyo, section I, vol. 14 , pp. 293–312, and vol. 16 , pp. 1–12. [REVIEW]A. S. Troelstra - 1971 - Journal of Symbolic Logic 36 (2):329-330.
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  34.  18
    An Interpretation of the Intuitionistic Propositional Calculus.John Dawson & A. S. Troelstra - 1990 - Journal of Symbolic Logic 55 (1):346-346.
  35.  31
    On the Intuitionistic Propositional Calculus.John Dawson & A. S. Troelstra - 1990 - Journal of Symbolic Logic 55 (1):344-344.
  36. [Omega]-Bibliography of Mathematical Logic.G. H. Müller, Wolfgang Lenski, Jane E. Kister, D. van Dalen & A. S. Troelstra - 1987
     
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  37.  18
    On a second order propositional operator in intuitionistic logic.A. A. Troelstra - 1981 - Studia Logica 40:113.
    This paper studies, by way of an example, the intuitionistic propositional connective * defined in the language of second order propositional logic by * ≡ ∃Q. In full topological models * is not generally definable but over Cantor-space and the reals it can be classically shown that *↔ ⅂⅂P; on the other hand, this is false constructively, i.e. a contradiction with Church's thesis is obtained. This is comparable with some well-known results on the completeness of intuitionistic first-order predicate logic. Over (...)
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  38. Logic and foundations of mathematics.D. van Dalen, J. G. Dijkman, A. Heyting, Stephen Cole Kleene & A. S. Troelstra (eds.) - 1969 - Groningen,: Wolters-Noordhoff.
  39.  65
    A. S. Troelstra and H. Schwichtenberg. Basic proof theory. Second edition of jsl lxiii 1605. Cambridge tracts in theoretical computer science, no. 43. cambridge university press, cambridge, new York, etc., 2000, XII + 417 pp. [REVIEW]Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.
  40.  64
    Basic proof theory, A.S. Troelstra and H. Schwichtenberg.Harold Schellinx - 1998 - Journal of Logic, Language and Information 7 (2):221-223.
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  41.  65
    Feferman Solomon. A language and axioms for explicit mathematics. Algebra and logic, Papers from the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia, edited by Crossley J. N., Lecture notes in mathematics, vol. 450, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 87–139.Feferman Solomon. Constructive theories of functions and classes. Logic colloquium '78, Proceedings of the colloquium held in Mons, August 1978, edited by Boffa Maurice, van Dalen Dirk, and McAloon Kenneth, Studies in logic and the foundations of mathematics, vol. 97, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1979, pp. 159–224. [REVIEW]G. R. Renardel de Lavalette & A. S. Troelstra - 1984 - Journal of Symbolic Logic 49 (1):308-311.
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  42. A.S. TROELSTRA "Choice sequences. A chapter of intuitionistic mathematics". [REVIEW]R. E. Grandy - 1983 - History and Philosophy of Logic 4 (2):241.
  43.  69
    A. S. Troelstra. Realizability. Handbook of proof theory, edited by Samuel R. Buss, Studies in logic and the foundations of mathematics, vol. 137, Elsevier, Amsterdam etc. 1998, pp. 407–473. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):470-471.
  44.  71
    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.
  45.  70
    A. S. Troelstra and H. Schwichtenberg. Basic proof theory. Cambridge tracts in theoretical computer science, no. 43. Cambridge University Press, Cambridge, New York, and Oakleigh, Victoria, 1996, xi + 343 pp. [REVIEW]Roy Dyckhoff - 1998 - Journal of Symbolic Logic 63 (4):1605-1606.
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  46. A.S. Troelstra, Lectures On Linear Logic. [REVIEW]Alasdair Urquhart - 1993 - Philosophy in Review 13:126-128.
     
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  47.  67
    (1 other version)Review: A. S. Troelstra, On Intermediate Propositional Logics. [REVIEW]Toshio Umezawa - 1968 - Journal of Symbolic Logic 33 (4):607-607.
  48.  27
    Review of A. S. Troelstra and D. van Dalen, Constructivism in Mathematics: An Introduction[REVIEW]Fred Richman - 1994 - Philosophia Mathematica 2 (1):86-89.
  49.  81
    Review: Kurt Godel, John Dawson, An Interpretation of the Intuitionistic Propositional Calculus (1933f); A. S. Troelstra, Introductory Note to 1933f. [REVIEW]Martin Davis - 1990 - Journal of Symbolic Logic 55 (1):346-346.
  50.  45
    Jean-Yves Girard. Linear logic. Theoretical computer science, vol. 50 , pp. 1–101. - A. S. Troelstra. Lectures on linear logic. CSLI lecture notes, no. 29. Center for the Study of Language and Information, Stanford 1992, also distributed by Cambridge University Press, New York, ix + 200 pp. [REVIEW]Herman Ruge Jervell - 1996 - Journal of Symbolic Logic 61 (1):336-338.
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