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The completeness of Heyting first-order logic

Published online by Cambridge University Press:  12 March 2014

W. W. Tait
W. W. Tait*
Affiliation:
5522 S. Everett Ave., Chicago, IL 60637, USA, E-mail: wwtx@uchicago.edu
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Abstract

Restricted to first-order formulas, the rules of inference in the Curry-Howard type theory are equivalent to those of first-order predicate logic as formalized by Heyting, with one exception: ∃-elimination in the Curry-Howard theory, where ∃x: A,F(x) is understood as disjoint union, are the projections, and these do not preserve first-orderedness. This note shows, however, that the Curry-Howard theory is conservative over Heyting's system.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 3 , September 2003 , pp. 751 - 763
Copyright
Copyright © Association for Symbolic Logic 2003

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References

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