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September 2003 The completeness of Heyting first-order logic
W. W. Tait
J. Symbolic Logic 68(3): 751-763 (September 2003). DOI: 10.2178/jsl/1058448436

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.

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W. W. Tait. "The completeness of Heyting first-order logic." J. Symbolic Logic 68 (3) 751 - 763, September 2003. https://doi.org/10.2178/jsl/1058448436

Information

Published: September 2003
First available in Project Euclid: 17 July 2003

zbMATH: 1055.03036
MathSciNet: MR2004G:03105
Digital Object Identifier: 10.2178/jsl/1058448436

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 3 • September 2003
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