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  1. A. S. Troelstra (2000). Basic Proof Theory. 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 (...)
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  2. A. S. Troelstra (2000). Realizability. Bulletin of Symbolic Logic 6 (4):470-471.
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  3. A. S. Troelstra (1999). Marginalia on Sequent Calculi. 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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  4. A. S. Troelstra (1998). Concepts and Axioms. 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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  5. A. S. Troelstra (1995). Natural Deduction for Intuitionistic Linear Logic. 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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  6. A. S. Troelstra (1991). Lectures on Linear Logic. Monograph Collection (Matt - Pseudo).
     
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  7. A. S. Troelstra & D. van Dalen (1991). Constructivism in Mathematics, Volume 2. Studia Logica 50 (2):355-356.
     
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  8. John Dawson & A. S. Troelstra (1990). An Interpretation of the Intuitionistic Propositional Calculus. Journal of Symbolic Logic 55 (1):346-346.
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  9. John Dawson & A. S. Troelstra (1990). On the Intuitionistic Propositional Calculus. Journal of Symbolic Logic 55 (1):344-344.
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  10. A. S. Troelstra (1990). Review: A. G. Dragalin, E. Mendelson, Mathematical Intuitionism. Introduction to Proof Theory. [REVIEW] Journal of Symbolic Logic 55 (3):1308-1309.
  11. A. S. Troelstra & D. van Dalen (1990). Construction in Mathematics. An Introduction, Volume 1. Studia Logica 49 (1):151-152.
     
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  12. A. S. Troelstra (1988). Constructivism in Mathematics: An Introduction. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
    Provability, Computability and Reflection.
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  13. G. H. Müller, Wolfgang Lenski, Jane E. Kister, D. van Dalen & A. S. Troelstra (1987). [Omega]-Bibliography of Mathematical Logic.
     
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  14. A. S. Troelstra (1986). Strong Normalization for Typed Terms with Surjective Pairing. Notre Dame Journal of Formal Logic 27 (4):547-550.
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  15. A. S. Troelstra (1985). Choice Sequences and Informal Rigour. 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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  16. G. R. Renardel de Lavalette & A. S. Troelstra (1984). 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] Journal of Symbolic Logic 49 (1):308-311.
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  17. J. Diller & A. S. Troelstra (1984). Realizability and Intuitionistic Logic. Synthese 60 (2):253 - 282.
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  18. A. S. Troelstra (1983). Analysing Choice Sequences. Journal of Philosophical Logic 12 (2):197 - 260.
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  19. L. E. J. Brouwer, A. S. Troelstra & D. van Dalen (eds.) (1982). The L.E.J. Brouwer Centenary Symposium: Proceedings of the Conference Held in Noordwijkerhout, 8-13 June 1981. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
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  20. A. S. Troelstra (1981). On a Second Order Propositional Operator in Intuitionistic Logic. 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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  21. A. S. Troelstra (1977). Choice Sequences: A Chapter of Intuitionistic Mathematics. Clarendon Press.
  22. A. S. Troelstra (1977). Some Models for Intuitionistic Finite Type Arithmetic with Fan Functional. Journal of Symbolic Logic 42 (2):194-202.
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  23. A. S. Troelstra (1975). Axioms for Intuitionistic Mathematics Incompatible with Classical Logic. Mathematisch Instituut.
     
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  24. A. S. Troelstra (1975). Principles of Intuitionism. Lectures Presented at the Summer Conference on Intuitionism and Proof Theory at SUNY at Buffalo, N.Y. [REVIEW] Journal of Symbolic Logic 40 (3):447-448.
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  25. A. S. Troelstra (1974). Note on the Fan Theorem. Journal of Symbolic Logic 39 (3):584-596.
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  26. A. S. Troelstra (1974). Review: Bruno Scarpellini, Proof Theory and Intuitionistic Systems. [REVIEW] Journal of Symbolic Logic 39 (3):607-609.
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  27. A. S. Troelstra (1973). Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. New York,Springer.
  28. A. S. Troelstra, B. van Rootselaar & J. F. Staal (1973). The Theory of Choice Sequences. Journal of Symbolic Logic 38 (2):332-332.
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  29. A. S. Troelstra (1972). Review: Mariko Yasugi, Intuitionistic Analysis and Godel's Interpretation. [REVIEW] Journal of Symbolic Logic 37 (2):404-404.
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  30. A. S. Troelstra (1971). An Addendum. Annals of Mathematical Logic 3 (4):437-439.
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  31. A. S. Troelstra (1971). Review: Tsutomu Hosoi, On Intermediate Logics. [REVIEW] Journal of Symbolic Logic 36 (2):329-330.
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  32. G. Kreisel & A. S. Troelstra (1970). Formal Systems for Some Branches of Intuitionistic Analysis. Annals of Mathematical Logic 1 (3):229-387.
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  33. D. Van Dalen & A. S. Troelstra (1970). Projections of Lawless Sequences. In A. Kino, John Myhill & Richard Eugene Vesley (eds.), Intuitionism and Proof Theory. Amsterdam,North-Holland Pub. Co..
     
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  34. A. S. Troelstra (1969). Informal Theory of Choice Sequences. Studia Logica 25 (1):31 - 54.
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  35. A. S. Troelstra (1969). Nieformalna Teoria Ciągów Z Wyboru. Studia Logica 25 (1):53-53.
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  36. A. S. Troelstra (1968). On Intermediate Propositional Logics. Journal of Symbolic Logic 33 (4):607-607.
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  37. A. S. Troelstra (1968). Review: Takashi Nagashima, An Extension of the Craig-Schutte Interpolation Theorem. [REVIEW] Journal of Symbolic Logic 33 (2):291-292.
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  38. A. S. Troelstra (1968). Review: Toshio Umezawa, On Logics Intermediate Between Intuitionistic and Classical Predicate Logic. [REVIEW] Journal of Symbolic Logic 33 (4):607-607.
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  39. D. van Dalen, J. G. Dijkman, A. Heyting, Stephen Cole Kleene & A. S. Troelstra (1968). Logic and Foundations of Mathematics. Wolters-Noordhoff.
     
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