{"paper":{"title":"Ramsey for $\\mathcal{R}_{1}$ ultrafilter mappings and their Dedekind cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Timothy Trujillo","submitted_at":"2014-01-13T13:43:23Z","abstract_excerpt":"Associated to each ultrafilter $\\mathcal{U}$ on $\\omega$ and each map $p:\\omega\\rightarrow \\omega$ is a Dedekind cut in the ultrapower $\\omega^{\\omega}/p( \\mathcal{U})$. Blass has characterized, under CH, the cuts obtainable when $\\mathcal{U}$ is taken to be either a p-point ultrafilter, a weakly-Ramsey ultrafilter or a Ramsey ultrafilter.\n  Dobrinen and Todorcevic have introduced the topological Ramsey space $\\mathcal{R}_{1}$. Associated to the space $\\mathcal{R}_{1}$ is a notion of Ramsey ultrafilter for $\\mathcal{R}_{1}$ generalizing the familiar notion of Ramsey ultrafilter on $\\omega$. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2835","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"}