English

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 IPC\mathbf{IPC}, the intuitionistic propositional calculus, and of logics weaker than IPC\mathbf{IPC} (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}
}