Filtrations for $\mathbb{wK4}$ and its relatives

Andrey Kudinov, Ilya Shapirovsky

Published 2023-12-31Version 1

We study the finite model property of subframe logics with expressible transitive closure modality. For $m>0$, let $\mathrm{L}_m$ be the logic given by axiom $\lozenge^{m+1} p\to \lozenge p\vee p$. We construct filtrations for the logics $\mathrm{L}_m$. It follows that these logics and their tense counterparts have the finite model property. Then we show that every canonical subframe logic that contains $\mathrm{L}_m$ have the finite model property.