Choice-free Topological Duality for Implicative Lattices and Heyting Algebras
Logic
2023-10-04 v1 Logic in Computer Science
Abstract
We develop a common semantic framework for the interpretation both of , the intuitionistic propositional calculus, and of logics weaker than (substructural and subintuitionistic logics). This is done by proving a choice-free representation and duality theorem for implicative lattices, which may or may not be distributive. The duality specializes to a choice-free duality for the category of Heyting algebras and a category of topological sorted frames with a ternary sorted relation.
Keywords
Cite
@article{arxiv.2302.03674,
title = {Choice-free Topological Duality for Implicative Lattices and Heyting Algebras},
author = {Chrysafis Hartonas},
journal= {arXiv preprint arXiv:2302.03674},
year = {2023}
}