An algebraic approach to canonical formulas: Intuitionistic case

Review of Symbolic Logic 2 (3):517-549 (2009)
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 (, , 0) homomorphisms, and ( , s 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 Zakharyaschev’s theorem that each intermediate logic can be axiomatized by canonical formulas
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