{"paper":{"title":"Minimal elementary end extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"James H. Schmerl","submitted_at":"2015-12-21T03:05:41Z","abstract_excerpt":"Suppose that ${\\mathcal M}$ is a model of PA and ${\\mathcal N}$ is a countably generated elementary end extension of ${\\mathcal M}$. Let ${\\mathfrak X}$ be the set of subsets of M that are coded by ${\\mathcal N}$. Then ${\\mathcal M}$ has a minimal elementary end extension that codes exactly the same subsets of M that ${\\mathcal N}$ does iff every set that is $\\Pi_1^0$-definable in $({\\mathcal M},{\\mathfrak X})$ is the union of countably many sets that are $\\Sigma_1^0$-definable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06478","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"}