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Choice-free topological duality for implicative lattices and Heyting algebras

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Abstract

We develop a common semantic framework for the interpretation both of \({\textbf {IPC}}\), the intuitionistic propositional calculus, and of logics weaker than \({\textbf {IPC}}\) (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.

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  1. Department of Digital Systems, University of Thessaly, Larissa, Greece

    Chrysafis Hartonas

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Hartonas, C. Choice-free topological duality for implicative lattices and Heyting algebras. Algebra Univers. 85, 3 (2024). https://doi.org/10.1007/s00012-023-00830-8

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