Topological Completeness for Higher-Order Logic

  • Steve Awodey
  • Carsten 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.
How to Cite
Awodey, S., & Butz, C. (1997). Topological Completeness for Higher-Order Logic. BRICS Report Series, 4(21).