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 K+□(□np→p)→□p (n≥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.