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Effectively constructible fixed points in Sacchetti's modal logics of provability (1811.12827v2)
Published 30 Nov 2018 in math.LO
Abstract: We give a purely syntactical proof of the fixed point theorem for Sacchetti's modal logics ${\bf K} + \Box(\Boxn p \to p) \to \Box p$ ($n \geq 2$) 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.