{"paper":{"title":"Topological Ramsey spaces and metrically Baire sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jose G. Mijares, Natasha Dobrinen","submitted_at":"2014-06-23T21:29:13Z","abstract_excerpt":"We characterize a class of topological Ramsey spaces such that each element $\\mathcal R$ of the class induces a collection $\\{\\mathcal R_k\\}_{k<\\omega}$ of projected spaces which have the property that every Baire set is Ramsey. Every projected space $\\mathcal R_k$ is a subspace of the corresponding space of length-$k$ approximation sequences with the Tychonoff, equivalently metric, topology.\n  This answers a question of S. Todorcevic and generalizes the results of Carlson \\cite{Carlson}, Carlson-Simpson \\cite{CarSim2}, Pr\\\"omel-Voigt \\cite{PromVoi}, and Voigt \\cite{Voigt}. We also present a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6918","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"}