{"paper":{"title":"A note on $\\aleph_{\\alpha}$-saturated o-minimal expansions of real closed fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Paola D'Aquino, Salma Kuhlmann","submitted_at":"2011-12-17T19:10:17Z","abstract_excerpt":"We give necessary and sufficient conditions for a polynomially bounded o-minimal expansion of a real closed field (in a language of arbitrary cardinality) to be $\\aleph_{\\alpha}$-saturated. The conditions are in terms of the value group, residue field, and pseudo- Cauchy sequences of the natural valuation on the real closed field. This is achieved by an analysis of types, leading to the trichotomy. Our characterization provides a construction method for saturated models, using fields of generalized power series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4078","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"}