{"paper":{"title":"On a question of Krajewski's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Albert Visser, Fedor Pakhomov","submitted_at":"2017-12-05T15:27:42Z","abstract_excerpt":"In this paper we provide a (negative) solution to a problem posed by Stanis{\\l}aw Krajewski. Consider a recursively enumerable theory U and a finite expansion of the signature of U that contains at least one predicate symbol of arity $\\ge$ 2. We show that, for any finite extension $\\alpha$ of U in the expanded language that is conservative over U, there is a conservative extension $\\beta$ of U in the expanded language, such that $\\alpha\\vdash\\beta$ and $\\beta\\nvdash\\alpha$. The result is preserved when we consider either extensions or model-conservative extensions of U in stead of conservative"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01713","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"}