Modal logics of finite direct powers of $\omega$ have the finite model property

Ilya Shapirovsky

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arXiv · 1903.04614

Modal logics of finite direct powers of $\omega$ have the finite model property

Ilya Shapirovsky

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Abstract

Let $(\omega^n,\preceq)$ be the direct power of $n$ instances of $(\omega,\leq)$, natural numbers with the standard ordering, $(\omega^n,\prec)$ the direct power of $n$ instances of $(\omega,<)$. We show that for all finite $n$, the modal logics of $(\omega^n,\preceq)$ and of $(\omega^n,\prec)$ have the finite model property and moreover, the modal algebras of the frames $(\omega^n,\preceq)$ and $(\omega^n,\prec)$ are locally finite.

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BibTeX RIS

Ilya Shapirovsky. 2019-03-11. Modal logics of finite direct powers of $\omega$ have the finite model property. https://arxiv.org/abs/1903.04614

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