Topological Completeness for Higher-Order Logic

Steve Awodey
Carsten Butz

July 1997


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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