Journal of Symbolic Logic

Topological Completeness for Higher-Order Logic

S. Awodey and C. Butz

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746174

Mathematical Reviews number (MathSciNet)
MR1791369

Zentralblatt MATH identifier
0977.03010

JSTOR
links.jstor.org

Citation

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


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