Choice-free topological duality for implicative lattices and Heyting algebras.

We develop a common semantic framework for the interpretation both of IPC , the intuitionistic propositional calculus, and of logics weaker than IPC (substructural and subintuitionistic logics). To this end, we prove 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 full subcategory of Heyting algebras and a category of topological sorted frames with a ternary sorted relation. [ABSTRACT FROM AUTHOR]