{"paper":{"title":"A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GN"],"primary_cat":"math.LO","authors_text":"Natasha Dobrinen, Stevo Todorcevic","submitted_at":"2012-05-26T19:14:06Z","abstract_excerpt":"Motivated by Tukey classification problems and building on work in \\cite{Dobrinen/Todorcevic11}, we develop a new hierarchy of topological Ramsey spaces $\\mathcal{R}_{\\alpha}$, $\\alpha<\\omega_1$. These spaces form a natural hierarchy of complexity, $\\mathcal{R}_0$ being the Ellentuck space, and for each $\\alpha<\\omega_1$, $\\mathcal{R}_{\\alpha+1}$ coming immediately after $\\mathcal{R}_{\\alpha}$ in complexity. Associated with each $\\mathcal{R}_{\\alpha}$ is an ultrafilter $\\mathcal{U}_{\\alpha}$, which is Ramsey for $\\mathcal{R}_{\\alpha}$, and in particular, is a rapid p-point satisfying certain p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5909","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"}