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Yuto Takeda

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Preprint Aug 2026

Frame definability in second-order arithmetic

We study the reverse-mathematical strength of frame definability in modal logic. The central principle is the Valuation Extension Lemma (VEL), which asserts that every assignment of propositional variables on a frame extends to a full valuation. We show that, over $\mathrm{RCA}_0$, VEL is equivalent to $\mathrm{ACA}^{+...

Yuto Takeda · 0 citations