Esakia's theorem for the amended monadic intuitionistic calculus

Abstract

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