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The logic of first order intuitionistic type theory with weak sigma-elimination

Published online by Cambridge University Press:  12 March 2014

M. D. G. Swaen
M. D. G. Swaen*
Affiliation:
Fakulteit Wiskunde en Informatika, Universiteit van Amsterdam, 1018 TV Amsterdam, The Netherlands
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Abstract

Via the formulas-as-types embedding certain extensions of Heyting Arithmetic can be represented in intuitionistic type theories. In this paper we discuss the embedding of ω-sorted Heyting Arithmetic HAω into a type theory WL, that can be described as Troelstra's system with so-called weak Σ-elimination rules. By syntactical means it is proved that a formula is derivable in HAω if and only if its corresponding type in WL is inhabited. Analogous results are proved for Diller's so-called restricted system and for a type theory based on predicate logic instead of arithmetic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 2 , June 1991 , pp. 467 - 483
Copyright
Copyright © Association for Symbolic Logic 1991

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References

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