{"paper":{"title":"Truth, Disjunction, and Induction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ali Enayat, Fedor Pakhomov","submitted_at":"2018-05-24T20:43:47Z","abstract_excerpt":"By a well-known result of Kotlarski, Krajewski, and Lachlan (1981), first-order Peano arithmetic $PA$ can be conservatively extended to the theory $CT^{-}[PA]$ of a truth predicate satisfying compositional axioms, i.e., axioms stating that the truth predicate is correct on atomic formulae and commutes with all the propositional connectives and quantifiers. This results motivates the general question of determining natural axioms concerning the truth predicate that can be added to $CT^{-}[PA]$ while maintaining conservativity over $PA$. Our main result shows that conservativity fails even for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09890","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"}