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Working paper

Gerald Berger, Lev D. Beklemishev, Hans Tompits. A many-sorted variant of Japaridze's polymodal provability logic, Jan 2016, 15 pp., ArXiv: 1601.02857.

arxiv.org. math. Cornell University, 2016. No. 1601.02857.
Berger G., Beklemishev L. D., Tompits H.
We consider a many-sorted variant of Japaridze's polymodal provability logic GLP. In this variant, propositional variables are assigned sorts n< omega, where variables of sort n are arithmetically interpreted as Pi_{n+1}-sentences of the arithmetical hierarchy. We prove that the many-sorted variant is arithmetically complete with respect to this interpretation.