{"paper":{"title":"On provability logics with linearly ordered modalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Fern\\'andez-Duque, Joost J. Joosten, Lev D. Beklemishev","submitted_at":"2012-10-17T18:14:23Z","abstract_excerpt":"We introduce the logics GLP(\\Lambda), a generalization of Japaridze's polymodal provability logic GLP(\\omega) where \\Lambda is any linearly ordered set representing a hierarchy of provability operators of increasing strength.\n  We shall provide a reduction of these logics to GLP(\\omega) yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP(\\Lambda) and the decidability of GLP(\\Lambda) for recursive orderings \\Lambda. Further, we give a restricted axiomatization of the variable-free fragment of GLP(\\Lambda)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4809","kind":"arxiv","version":1},"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"}