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

Taishi Kurahashi, Yuya Okawa

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,…