An open mapping theorem for finitely copresented Esakia spaces
arXiv:1710.01630 · doi:10.1016/j.topol.2018.03.006
Abstract
We prove an open mapping theorem for the topological spaces dual to finitely presented Heyting algebras. This yields in particular a short, self-contained semantic proof of the uniform interpolation theorem for intuitionistic propositional logic, first proved by Pitts in 1992. Our proof is based on the methods of Ghilardi & Zawadowski. However, our proof does not require sheaves nor games, only basic duality theory for Heyting algebras.
8 pages. Minor changes in presentation. To appear in Topology and its Applications