45 found
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  1.  80
    Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.
    This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much (...)
  2.  34
    Constructivism in Mathematics: An Introduction.A. S. Troelstra - 1988 - Elsevier.
    Provability, Computability and Reflection.
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  3.  43
    Metamathematical Investigation of Intuitionistic Arithmetic and Analysis.A. S. Troelstra - 1973 - New York: Springer.
  4. Lectures on Linear Logic.A. S. Troelstra - 1991
     
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  5.  20
    Choice Sequences: A Chapter of Intuitionistic Mathematics.A. S. Troelstra - 1977 - Clarendon Press.
  6.  9
    Realizability.A. S. Troelstra - 2000 - Bulletin of Symbolic Logic 6 (4):470-471.
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  7.  68
    Realizability and Intuitionistic Logic.J. Diller & A. S. Troelstra - 1984 - Synthese 60 (2):253 - 282.
  8. 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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  9.  36
    Analysing Choice Sequences.A. S. Troelstra - 1983 - Journal of Philosophical Logic 12 (2):197 - 260.
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  10.  14
    Note on the Fan Theorem.A. S. Troelstra - 1974 - Journal of Symbolic Logic 39 (3):584-596.
  11.  15
    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.
  12.  12
    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.
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  13.  11
    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.
  14.  5
    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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  15.  41
    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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  16.  16
    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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  17.  9
    Bruno Scarpellini. Proof Theory and Intuitionistic Systems. Lecture Notes in Mathematics, No. 212. Springer-Verlag, Berlin, Heidelberg, and New York, 1971, VII + 291 Pp. [REVIEW]A. S. Troelstra - 1974 - Journal of Symbolic Logic 39 (3):607-609.
  18.  29
    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.
  19.  27
    Informal Theory of Choice Sequences.A. S. Troelstra - 1969 - Studia Logica 25 (1):31 - 54.
  20.  51
    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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  21.  29
    Nieformalna Teoria Ciągów Z Wyboru.A. S. Troelstra - 1969 - Studia Logica 25 (1):53-53.
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  22. Constructivism in Mathematics, Volume 2.A. S. Troelstra & D. van Dalen - 1991 - Studia Logica 50 (2):355-356.
     
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  23.  23
    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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  24. Projections of Lawless Sequences.D. Van Dalen & A. S. Troelstra - 1970 - In A. Kino, John Myhill & Richard Eugene Vesley (eds.), Intuitionism and Proof Theory. Amsterdam: North-Holland Pub. Co..
     
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  25. History of Constructivism in the 20th Century Vol. Ml-91-05.A. S. Troelstra - 1991 - University of Amsterdam.
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  26.  6
    An Addendum.A. S. Troelstra - 1971 - Annals of Pure and Applied Logic 3 (4):437.
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  27.  15
    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.
  28. The Discovery of E.W. Beth’s Semantics for Intuitionistic Logic.A. S. Troelstra & P. van Ulsen - 1999 - In J. Gerbrandy, M. Marx, M. de Rijke & Y. Venema (eds.), Jfak. Essays Dedicated to Johan van Benthem on the Occasion of His 50th Birthday. Vossiuspers, Amsterdam University Press.
     
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  29.  13
    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.
  30.  13
    Principles of Intuitionism. Lectures Presented at the Summer Conference on Intuitionism and Proof Theory at SUNY at Buffalo, N.Y. [REVIEW]A. S. Troelstra - 1975 - Journal of Symbolic Logic 40 (3):447-448.
  31. Construction in Mathematics. An Introduction, Volume 1.A. S. Troelstra & D. van Dalen - 1990 - Studia Logica 49 (1):151-152.
     
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  32.  16
    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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  33.  7
    An Interpretation of the Intuitionistic Propositional Calculus.John Dawson & A. S. Troelstra - 1990 - Journal of Symbolic Logic 55 (1):346-346.
  34.  7
    On the Intuitionistic Propositional Calculus.John Dawson & A. S. Troelstra - 1990 - Journal of Symbolic Logic 55 (1):344-344.
  35.  8
    Review: Tsutomu Hosoi, On Intermediate Logics. [REVIEW]A. S. Troelstra - 1971 - Journal of Symbolic Logic 36 (2):329-330.
  36.  6
    Review: Solomon Feferman, J. N. Crossley, A Language and Axioms for Explicit Mathematics; Solomon Feferman, Maurice Boffa, Dirk van Dalen, Kenneth McAloon, Constructive Theories of Functions and Classes. [REVIEW]G. R. Renardel de Lavalette & A. S. Troelstra - 1984 - Journal of Symbolic Logic 49 (1):308-311.
  37.  5
    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.
  38.  3
    Review: Mariko Yasugi, Intuitionistic Analysis and Godel's Interpretation. [REVIEW]A. S. Troelstra - 1972 - Journal of Symbolic Logic 37 (2):404-404.
  39.  3
    The Theory of Choice Sequences.A. S. Troelstra, B. van Rootselaar & J. F. Staal - 1973 - Journal of Symbolic Logic 38 (2):332-332.
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  40.  2
    Review: Bruno Scarpellini, Proof Theory and Intuitionistic Systems. [REVIEW]A. S. Troelstra - 1974 - Journal of Symbolic Logic 39 (3):607-609.
  41.  1
    Proof Theory and Intuitionistic Systems.A. S. Troelstra - 1974 - Journal of Symbolic Logic 39 (3):607-609.
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  42. 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 - Elsevier.
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  43. [Omega]-Bibliography of Mathematical Logic.G. H. Müller, Wolfgang Lenski, Jane E. Kister, D. van Dalen & A. S. Troelstra - 1987
     
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  44. Axioms for Intuitionistic Mathematics Incompatible with Classical Logic.A. S. Troelstra - 1975 - Mathematisch Instituut.
     
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  45. Logic and Foundations of Mathematics.D. van Dalen, J. G. Dijkman, A. Heyting, Stephen Cole Kleene & A. S. Troelstra - 1968 - Wolters-Noordhoff.