Finite axiomatization of $\textbf{GL}\times\textbf{S5}$ and $\textbf{Grz}\times\textbf{S5}$

Guram Bezhanishvili; Mashiath Khan

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arXiv · 2512.09381

Finite axiomatization of $\textbf{GL}\times\textbf{S5}$ and $\textbf{Grz}\times\textbf{S5}$

Guram Bezhanishvili·Mashiath Khan

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Abstract

We prove that $\mathbf{GL} \times \mathbf{S5}$ is product matching, and that $\mathbf{Grz} \times \mathbf{S5}$ is axiomatizable by adding to $[\mathbf{Grz},\mathbf{S5}]$ the G\"odel translation of the monadic Casari formula. This settles the question of the finite axiomatizability of these logics posed by Gabbay and Shehtman (1998).

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Guram Bezhanishvili, Mashiath Khan. 2025-12-10. Finite axiomatization of $\textbf{GL}\times\textbf{S5}$ and $\textbf{Grz}\times\textbf{S5}$. https://arxiv.org/abs/2512.09381

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