{"paper":{"title":"Metrically Ramsey ultrafilters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GN","authors_text":"Igor Protasov, Ksenia Protasova","submitted_at":"2017-04-25T09:43:48Z","abstract_excerpt":"Given a metric space $(X,d)$, we say that a mapping $\\chi: [X]^{2}\\longrightarrow\\{0.1\\}$ is an isometric coloring if $d(x,y)=d(z,t)$ implies $\\chi(\\{x,y\\})=\\chi(\\{z,t\\})$. A free ultrafilter $\\mathcal{U}$ on an infinite metric space $(X,d)$ is called metrically Ramsey if, for every isometric coloring $\\chi$ of $[X]^{2}$, there is a member $U\\in\\mathcal{U}$ such that the set $[U]^{2}$ is $\\chi$-monochrome. We prove that each infinite ultrametric space $(X,d)$ has a countable subset $Y$ such that each free ultrafilter $\\mathcal{U}$ on $X$ satisfying $Y\\in\\mathcal{U}$ is metrically Ramsey. On th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07824","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"}