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Deductive systems and categories III. Cartesian closed categories, intuitionist propositional calculus, and combinatory logic

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Toposes, Algebraic Geometry and Logic

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References

  • A. Church, The calculi of lambda-conversion, Annals of Math. Studies 6, Princeton University Press, Princeton 1941.

    Google Scholar 

  • H.B. Curry and R. Feys, Combinatory Logic, Vol. 1, North-Holland Publ. Co., Amsterdam 1958.

    Google Scholar 

  • S. Eilenberg and G.M. Kelly, Closed categories, Proc. Conference Categorical Algebra, La Jolla 1965, pp. 421–562, Springer-Verlag, New York 1966.

    Chapter  Google Scholar 

  • T.Fox, Combinatory Logic and cartesian closed categories, M.Sc. Thesis, McGill University 1970.

    Google Scholar 

  • K.Gödel, On formally undecidable propositions, reproduced in J. van Heijenoort, From Frege to Gödel, pp. 592–617, Cambridge 1967.

    Google Scholar 

  • J. Lambek, Deductive Systems and Categories I, Math. Systems Theory 2 (1958), 287–318.

    Article  MathSciNet  Google Scholar 

  • J. Lambek, Deductive Systems and Categories II, Lecture Notes in Mathematics 86, pp. 76–122, Springer-Verlag, Berlin 1969.

    Google Scholar 

  • F.W.Lawvere, A functional analysis of logical operations, undated manuscript.

    Google Scholar 

  • F.W. Lawvere, Functorial semantics of elementary theories, abstract. J.Symbolic Logic 31 (1966), 294–295.

    Google Scholar 

  • F.W. Lawvere, Theories as categories and the completeness theorem, abstract, J.Symbolic Logic 32 (1967), 562.

    Google Scholar 

  • F.W. Lawvere, Diagonal arguments and cartesian closed categories, Lecture Notes in Mathematics 92, pp. 134–145, Springer-Verlag, Berlin 1969.

    Google Scholar 

  • F.W. Lawvere, Adjointness in foundations, Dialectica 23 (1969), 281–296.

    Article  MATH  Google Scholar 

  • F.W. Lawvere, Equality in hyperdoctrines and comprehension schema as an adjoint functor, Proc.Symp.Pure Math. 17, pp. 1–14, Amer.Math.Society, Rhode Island 1970.

    Google Scholar 

  • F.W.Lawvere, Category-valued higher logic, Dialectica, to appear.

    Google Scholar 

  • P.C. Rosenbloom, The elements of mathematical logic, Dover Publications, New York 1950.

    MATH  Google Scholar 

  • M.Schönfinkel, On the building blocks of mathematical logic, reproduced in J. van Heijenoort, From Frege to Gödel, pp. 355–366, Cambridge 1967.

    Google Scholar 

  • M.E.Szabo, Proof-theoretic investigations in categorical algebra, Ph.D.Thesis, McGill University 1970.

    Google Scholar 

  • M.E.Szabo, A categorical equivalence of proofs, to appear.

    Google Scholar 

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F. W. Lawvere

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Lambek, J. (1972). Deductive systems and categories III. Cartesian closed categories, intuitionist propositional calculus, and combinatory logic. In: Lawvere, F.W. (eds) Toposes, Algebraic Geometry and Logic. Lecture Notes in Mathematics, vol 274. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073965

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  • DOI: https://doi.org/10.1007/BFb0073965

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  • Print ISBN: 978-3-540-05920-2

  • Online ISBN: 978-3-540-37609-5

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