Failure of Esakia's theorem in the monadic setting
Logic
2025-12-09 v2
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.
Cite
@article{arxiv.2409.05607,
title = {Failure of Esakia's theorem in the monadic setting},
author = {Guram Bezhanishvili and Luca Carai},
journal= {arXiv preprint arXiv:2409.05607},
year = {2025}
}