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

Abstract

We give a purely syntactical proof of the fixed point theorem for Sacchetti's modal logics $\mathbf{K}+\square ({\square }^{n}p\to p)\to \square p$ ($n\ge 2$) 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.

arXiv comment19 pages