{"paper":{"title":"Trakhtenbrot theorem and first-order axiomatic extensions of MTL","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Matteo Bianchi","submitted_at":"2014-03-04T15:25:34Z","abstract_excerpt":"In 1950, B.A. Trakhtenbrot showed that the set of first-order tautologies associated to finite models is not recursively enumerable. In 1999, P. H\\'ajek generalized this result to the first-order versions of \\L ukasiewicz, G\\\"odel and Product logics. In this paper we extend the analysis to the first-order axiomatic extensions of MTL. Our main result is the following. Let L be an axiomatic extension L of MTL s.t. TAUT$_\\text{L}$ is decidable, and whose corresponding variety is generated by a chain: for every generic L-chain $\\mathcal{A}$ the set fTAUT$^\\mathcal{A}_{\\forall}$ (the set of first-o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0812","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"}