{"paper":{"title":"Ruitenburg's Theorem via Duality and Bounded Bisimulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Luigi Santocanale (LIS), Silvio Ghilardi","submitted_at":"2018-04-17T09:38:43Z","abstract_excerpt":"For a given intuitionistic propositional formula A and a propositional variable x occurring in it, define the infinite sequence of formulae { A \\_i | i$\\ge$1} by letting A\\_1 be A and A\\_{i+1} be A(A\\_i/x). Ruitenburg's Theorem [8] says that the sequence { A \\_i } (modulo logical equivalence) is ultimately periodic with period 2, i.e. there is N $\\ge$ 0 such that A N+2 $\\leftrightarrow$ A N is provable in intuitionistic propositional calculus. We give a semantic proof of this theorem, using duality techniques and bounded bisimulations ranks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06130","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"}