Journal of Symbolic Logic

The completeness of Heyting first-order logic

W. W. Tait

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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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J. Symbolic Logic, Volume 68, Issue 3 (2003), 751- 763.

First available in Project Euclid: 17 July 2003

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Tait, W. W. The completeness of Heyting first-order logic. J. Symbolic Logic 68 (2003), no. 3, 751-- 763. doi:10.2178/jsl/1058448436.

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