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Topological Completeness for Higher-Order Logic

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journal contribution
posted on 21.11.1998, 00:00 by Steven AwodeySteven Awodey, C. Butz
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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21/11/1998

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