An open mapping theorem for finitely copresented Esakia spaces

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...

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Bibliographic Details
Published in:arXiv.org 2018-03
Main Authors: van Gool, Samuel J, Reggio, Luca
Format: Article
Language:English
Subjects:
Interpolation
Mapping
Sheaves
Theorems
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1710.01630