{"paper":{"title":"Finite Ramsey degrees and Fra\\\"iss\\'e expansions with the Ramsey property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lionel Nguyen Van Th\\'e","submitted_at":"2017-05-30T12:39:14Z","abstract_excerpt":"By a result of Zucker, every Fra\\\"iss\\'e structure $\\bf F$ for which the elements of $\\mathrm{Age}(\\bf F)$ have finite Ramsey degrees admits a Fra\\\"iss\\'e precompact expansion $\\bf F^{*}$ whose age $\\mathrm{Age}(\\bf F^{*})$ has the Ramsey property. While the original method uses dynamics in spaces of ultrafilters, the purpose of the present short note is to provide a different proof, based on classical tools from Fra\\\"iss\\'e theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10582","kind":"arxiv","version":2},"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"}