English

On the Provability Logic of HA

Logic 2026-01-05 v4

Abstract

We axiomatize the provability logic of \HA\HA and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics extending iK4. A principal technical tool is the introduction of a new type of semantics, termed \emph{provability models}, for modal logics extending iGL. This semantics combines elements of standard Kripke semantics with provability in propositional modal logics.

Keywords

Cite

@article{arxiv.2206.00445,
  title  = {On the Provability Logic of HA},
  author = {Mojtaba Mojtahedi},
  journal= {arXiv preprint arXiv:2206.00445},
  year   = {2026}
}