Topological Completeness for Higher-Order Logic

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 se...

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Veröffentlicht in:BRICS Report Series 1997-01, Vol.4 (21)
Hauptverfasser: Awodey, Steve, Butz, Carsten
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description 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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