Year: 2026
Type: preprint
Abstract: We prove that the polymodal logic $\mathsf{J}$ is strongly complete with respect to \textit{$\mathsf{J}$-bouquets}, a topological refinement of its Kripke semantics. In particular, it is strongly topologically complete. This yields the following completeness result for the provability logic $\mathsf{GLP}$: a countable set of formulae $Γ$ is consistent with $\mathsf{GLP}$ if and only if there is a $\mathsf{J}$-bouquet $B$ and $r\in B$ such that $B, r\Vdash \mathsf{GLP}$ and $B, r\VdashΓ$. In contrast, we exhibit counterexamples showing that $\mathsf{GLP}$ is not strongly complete with respect to Beklemishev-Gabelaia spaces.
Source: arXiv (Cornell University)
Authors: Aguilera, Juan P., Stepanov, Grigorii
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202138993
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