AN ALGEBRAIC APPROACH TO CANONICAL FORMULAS: INTUITIONISTIC CASE

We introduce partial Esakia morphisms, well partial Esakia morphisms, and strong partial Esakia morphisms between Esakia spaces and show that they provide the dual description of (A, homomorphisms, (A, 0) homomorphisms, and (A, v) homomorphisms between Heyting algebras, thus establishing a generalization of Esakia duality. This yields an algebraic characterization of Zakharyaschevʹs subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we obtain a new simplified proof (which is algebraic in nature) of Zakharyaschevʹs theorem that each intermediate logic can be axiomatized by canonical formulas.