English

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}
}
R2 v1 2026-06-28T18:38:30.782Z