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A characterization of ML in many-sorted arithmetic with conditional application

  • M. D. G. Swaen (a1)

Abstract

In this paper we discuss an interpretation of intuitionistic type theory in many-sorted arithmetic with so-called conditional application. Via the formulas-as-types correspondence the arithmetical system in turn can be embedded in ML, resulting in a characterization of strong Σ-elimination by an axiom of conditional choice.

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References

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Martin-Löf, P. [80], Intuitionistic type theory, Bibliopolis, Naples.
de Lavalette, G. R. Renardel [85], Theories with type-free application and extended bar-induction, Thesis, Universiteit van Amsterdam, Amsterdam.
Smith, J. M. [84], An interpretation of Martin-Löf's type theory in a type-free theory of propositions, this Journal, vol. 49, pp. 730753.
Swaen, M. D. G. [89], Weak and strong sum-elimination in intuitionistic type theory, Thesis, Universiteit van Amsterdam, Amsterdam.
Troelstra, A. S. (editor) [73], Metamathematical investigations of intuitionistic arithmetic and analysis, Lecture Notes in Mathematics, vol. 344, Springer-Verlag, Berlin.
Troelstra, A. S. and van Dalen, D. [88], Constructivism in mathematics. II, North-Holland, Amsterdam.

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