On Provability Logic of HA

TL;DR

This work axiomatize the provability logic of HA and show that it is decidable, and provides some sort of semantics, called provability semantics, for modal logics extending iGL, which is a mixture of usual Kripke semantics and provability in propositional modallogics.

Abstract

We axiomatize the provability logic of HA and show that it is decidable. Moreover we axiomatize the preservativity and relative admissibility for several modal logics extending iK4. As a main tool, we also provide some sort of semantics, called provability semantics, for modal logics extending iGL, which is a mixture of usual Kripke semantics and provability in propositional modal logics.