Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m+k} p \to \Box^m p$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916982709813248 |
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| author | Knudstorp, Søren Brinck |
| author_facet | Knudstorp, Søren Brinck |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00864 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m+k} p \to \Box^m p$ Knudstorp, Søren Brinck Logic 03B25, 03B45, 06E25 F.4.1 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. |
| title | Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m+k} p \to \Box^m p$ |
| topic | Logic 03B25, 03B45, 06E25 F.4.1 |
| url | https://arxiv.org/abs/2510.00864 |