Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m+k} p \to \Box^m p$

Søren Brinck Knudstorp

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arXiv · 2510.00864

Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m+k} p \to \Box^m p$

Søren Brinck Knudstorp

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Abstract

It is a long-standing open problem whether modal logics of the form $\mathbf{K} \oplus \Box^n p \to \Box^m p$ for $n>m>1$ have the finite model property (FMP). We solve this by showing that any modal logic axiomatized by formulas of the form $\Box^n p \to \Box^m p$ where $n>m>1$ has the FMP.

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BibTeX RIS

Søren Brinck Knudstorp. 2025-10-01. Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m+k} p \to \Box^m p$. https://arxiv.org/abs/2510.00864

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