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

Søren Brinck Knudstorp

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

Logic 2025-10-02 v1

Authors: Søren Brinck Knudstorp

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.

Keywords

modal logic finite model property box modality axiomatization model theory

Cite

@article{arxiv.2510.00864,
  title  = {Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m+k} p \to \Box^m p$},
  author = {Søren Brinck Knudstorp},
  journal= {arXiv preprint arXiv:2510.00864},
  year   = {2025}
}

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11 pages

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