Journal of Symbolic Logic

Topological Completeness for Higher-Order Logic

S. Awodey and C. Butz

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Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces-so-called "topological semantics". The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.

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J. Symbolic Logic, Volume 65, Issue 3 (2000), 1168-1182.

First available in Project Euclid: 6 July 2007

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Awodey, S.; Butz, C. Topological Completeness for Higher-Order Logic. J. Symbolic Logic 65 (2000), no. 3, 1168--1182.

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