{"paper":{"title":"Ideal games and Ramsey sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Carlos Di Prisco, Carlos Uzcategui, Jose G. Mijares","submitted_at":"2010-09-20T02:36:41Z","abstract_excerpt":"It is shown that Matet's characterization of the Ramsey property relative to a selective co-ideal $\\mathcal{H}$, in terms of games of Kastanas, still holds if we consider semiselectivity instead of selectivity. Moreover, we prove that a co-ideal $\\mathcal{H}$ is semiselective if and only if Matet's game-theoretic characterization of the $\\mathcal{H}$-Ramsey property holds. This lifts Kastanas's characterization of the classical Ramsey property to its optimal setting, from the point of view of the local Ramsey theory and gives a game-theoretic counterpart to a theorem of Farah \\cite{far}, asser"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3683","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"}