3 papers
math.LO2026
Frame definability in second-order arithmetic
Yuto Takeda
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 o…
math.LO2026
Bisimulations in second-order arithmetic
Yuto Takeda, Keita Yokoyama
This paper investigates the logical strength of two theorems in modal propositional logic - the Hennessy-Milner theorem and the van Benthem characterization theorem - within the fr…
math.LO2025
Completeness theorems for modal logic in second-order arithmetic
Sho Shimomichi, Yuto Takeda, Keita Yokoyama
This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theore…