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arXiv · 2604.25780

Finite Kripke models and provability interpretations in quantified modal logic

Haruka Kogure·Taishi Kurahashi
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Abstract

In this paper, we investigate arithmetical completeness with respect to finite Kripke models of quantified modal logic. We adapt the finite-model embedding techniques of Artemov and Japaridze to two settings involving finite Kripke models. First, for conversely well-founded finite Kripke models of quantified modal logic, we construct a $Σ_2$ Fefermanian provability predicate together with an arithmetical interpretation that embeds the model into arithmetic. Second, for finite constant domain Kripke models of quantified modal logic, we construct a $Σ_1$ provability predicate satisfying $\mathbf{D2^G}$ and an arithmetical interpretation yielding such an embedding.

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Haruka Kogure, Taishi Kurahashi. 2026-04-28. Finite Kripke models and provability interpretations in quantified modal logic. https://arxiv.org/abs/2604.25780

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