Esakia's theorem for the amended monadic intuitionistic calculus

TL;DR

This paper extends Esakia's theorem to the amended monadic intuitionistic calculus, establishing it as the largest modal companion of the amended monadic Grzegorczyk logic, unlike the standard monadic intuitionistic logic.

Contribution

It demonstrates that Esakia's theorem applies to the amended monadic intuitionistic calculus, identifying its largest modal companion, which was not possible for the standard monadic intuitionistic logic.

Findings

$ ext{M}^+ ext{Grz}$ is the largest modal companion of $ ext{M}^+ ext{IPC}$

Esakia's theorem extends to $ ext{M}^+ ext{IPC}$ but not to $ ext{MIPC}$

The amended monadic calculus has unique modal correspondence properties

Abstract

We show that the amended monadic Grzegorczyk logic $\mathsf{M^+Grz}$ is the largest modal companion of the amended monadic intuitionistic logic $\mathsf{M^+IPC}$. Thus, unlike the monadic intuitionistic logic $\mathsf{MIPC}$, Esakia's theorem does extend to $\mathsf{M^+IPC}$.