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Vollständigkeit und Schnittelimination in der Intuitionistischen Typenlogik

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Abstract

Sections 1 to 4 contain the strong completeness theorem of cut-free intuitionistic type theory relative to semi-Kripke-valuations, which gives the following corollaries: (1) The strong completeness theorem for intuitionistic type theory with cut rule relative to full Kripke-valuations. (2) A semantical eqivalent of cutelimination in intuitionistic type theory. Section 5 contains a proof of the cutelimination theorem and some corollaries to it.

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Literatur

  1. ACZEL, P.H.G.: Saturated intuitionistic theories, Contributions to the mathematical logic, North Holland, Amsterdam, 1–11, 1968.

    Google Scholar 

  2. FITTING, M.: Intuitionistic logic model theory and forcing, 1. Aufl., North Holland, Amsterdam 1969.

    MATH  Google Scholar 

  3. HENKIN, L.: Completeness in the theory of types, J. symbolic logic 15, 81–91, 1950.

    Article  MathSciNet  MATH  Google Scholar 

  4. KRIPKE S.: Semantical analysis of intuitionistic logic 1, in Formal systems and recursive functions, ed. J. Crossley and M. Dummet, North Holland, Amsterdam, 92–130, 1965.

    Chapter  Google Scholar 

  5. PRAWITZ, D.: Natural deduction, a proof theoretical study, 1. Aufl., Stockholm, 1965.

  6. PRAWITZ, D.: Hauptsatz for higher order logic, J. symbolic logic 33, 452–457, 1968.

    Article  MathSciNet  MATH  Google Scholar 

  7. PRAWITZ, D.: Some results for intuitionistic logic with second order quantification rules, Intuitionism and proof theory, North Holland, Amsterdam, 259–270, 1970.

    Google Scholar 

  8. SCHÜTTE, K.: Schlußweisenkalküle der Prädikatenlogik, Math. Ann. 122, 47–65, 1950.

    Article  MathSciNet  MATH  Google Scholar 

  9. SCHÜTTE, K.: Syntactical and semantical properties of simple type theory, J. symbolic logic 25, 305–326, 1960.

    Article  MathSciNet  MATH  Google Scholar 

  10. TAKAHASHI, M.: A proof of cut-elimination theorem in simple type theory, The journal of the mathematical society of Japan 19, 399–410, 1967.

    Article  MathSciNet  MATH  Google Scholar 

  11. TAKAHASHI, M.: Cut-elimination theorem and Brouwerian-valued models for intuitionistic type theory, Comment. math. universitatis Sancti Pauli, Tokyo, 1–18, 1970.

    Google Scholar 

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  1. Mathematisches Institut der Universität München, Schellingstra\e 2-8, 8 München 13

    Horst Osswald

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  1. Horst Osswald
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Osswald, H. Vollständigkeit und Schnittelimination in der Intuitionistischen Typenlogik. Manuscripta Math 6, 17–31 (1972). https://doi.org/10.1007/BF01298410

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  • DOI: https://doi.org/10.1007/BF01298410

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