{"paper":{"title":"Definable choice for a class of weakly o-minimal theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Christopher S. Shaw, Michael C. Laskowski","submitted_at":"2015-05-08T19:28:57Z","abstract_excerpt":"Given an o-minimal structure ${\\mathcal M}$ with a group operation, we show that for a properly convex subset $U$, the theory of the expanded structure ${\\mathcal M}'=({\\mathcal M},U)$ has definable Skolem functions precisely when ${\\mathcal M}'$ is valuational. As a corollary, we get an elementary proof that the theory of any such ${\\mathcal M}'$ does not satisfy definable choice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02147","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"}