{"paper":{"title":"A Many-Sorted Variant of Japaridze's Polymodal Provability Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Gerald Berger, Hans Tompits, Lev D. Beklemishev","submitted_at":"2016-01-12T13:44:27Z","abstract_excerpt":"We consider a many-sorted variant of Japaridze's polymodal provability logic $\\mathsf{GLP}$. In this variant, which is denoted $\\mathsf{GLP}^\\ast$, propositional variables are assigned sorts $\\alpha \\leq \\omega$, where variables of finite sort $n < \\omega$ are interpreted as $\\Pi_{n+1}$-sentences of the arithmetical hierarchy, while those of sort $\\omega$ range over arbitrary ones. We prove that $\\mathsf{GLP}^\\ast$ is arithmetically complete with respect to this interpretation. Moreover, we relate $\\mathsf{GLP}^\\ast$ to its one-sorted counterpart $\\mathsf{GLP}$ and prove that the former inheri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02857","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}