Topological Completeness for Higher-Order Logic

  • Steve Awodey
  • Carsten Butz

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.
Published
1997-01-21
How to Cite
Awodey, S., & Butz, C. (1997). Topological Completeness for Higher-Order Logic. BRICS Report Series, 4(21). https://doi.org/10.7146/brics.v4i21.18947