Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 65, Issue 3 (2000), 1168-1182.
Topological Completeness for Higher-Order Logic
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.
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. https://projecteuclid.org/euclid.jsl/1183746174