Failure of Esakia's theorem in the monadic setting

Guram Bezhanishvili; Luca Carai

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arXiv · 2409.05607

Failure of Esakia's theorem in the monadic setting

Guram Bezhanishvili·Luca Carai

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Abstract

Esakia's theorem states that Grzegorczyk's logic is the greatest modal companion of intuitionistic propositional calculus. We prove that already the one-variable fragment of intuitionistic predicate calculus does not have a greatest modal companion, yielding that Esakia's theorem fails in the monadic setting.

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Guram Bezhanishvili, Luca Carai. 2024-09-09. Failure of Esakia's theorem in the monadic setting. https://arxiv.org/abs/2409.05607

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