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

  • M. D. G. Swaen (a1)


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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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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