{"paper":{"title":"From abstract alpha-Ramsey theory to abstract ultra-Ramsey theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Timothy Trujillo","submitted_at":"2016-01-15T07:57:49Z","abstract_excerpt":"We work within the framework of the Alpha-Theory introduced by Benci and Di Nasso. The Alpha-Theory postulates a few natural properties for an infinite \"ideal\" number $\\alpha$. The formulation provides an elementary axiomatics for the methods of abstract ultra-Ramsey theory.\n  The main results are Theorem 10, Theorem 57, Theorem 67 and Theorem 73. Theorem 10 is an infinite-dimensional extension of the celebrated Ramsey's Theorem. We show that corollaries of this result include the Galvin-Pirky Theorem, the Silver Theorem and the $\\vec{\\alpha}$-Ellentuck Theorem. We prove that, under the assump"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03831","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"}