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arXiv · 1811.12827

Effectively constructible fixed points in Sacchetti's modal logics of provability

Taishi Kurahashi·Yuya Okawa
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Abstract

We give a purely syntactical proof of the fixed point theorem for Sacchetti's modal logics ${\bf K} + \Box(\Box^n p \to p) \to \Box p$ ($n \geq 2$) of provability. From our proof, an effective procedure for constructing fixed points in these logics is obtained. We also show the existence of simple fixed points for particular modal formulas.

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Taishi Kurahashi, Yuya Okawa. 2018-11-30. Effectively constructible fixed points in Sacchetti's modal logics of provability. https://arxiv.org/abs/1811.12827

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