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arXiv · 2405.09401

Failure of the Blok-Esakia Theorem in the monadic setting

Guram Bezhanishvili·Luca Carai
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Abstract

The Blok-Esakia Theorem establishes that the lattice of superintuitionistic logics is isomorphic to the lattice of extensions of Grzegorczyk's logic. We prove that the Blok-Esakia isomorphism $\sigma$ does not extend to the fragments of the corresponding predicate logics of already one fixed variable. In other words, we prove that $\sigma$ is no longer an isomorphism from the lattice of extensions of the monadic intuitionistic logic to the lattice of extensions of the monadic Grzegorczyk logic.

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BibTeXRIS

Guram Bezhanishvili, Luca Carai. 2024-05-15. Failure of the Blok-Esakia Theorem in the monadic setting. https://doi.org/10.1016/j.apal.2024.103527

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