An open mapping theorem for finitely copresented Esakia spaces
Logic
2020-11-19 v2 General Topology
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1710.01630,
title = {An open mapping theorem for finitely copresented Esakia spaces},
author = {Samuel J. van Gool and Luca Reggio},
journal= {arXiv preprint arXiv:1710.01630},
year = {2020}
}
Comments
8 pages. Minor changes in presentation. To appear in Topology and its Applications