{"paper":{"title":"Ramsey's theorem for singletons and strong computable reducibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Damir D. Dzhafarov, Linda Brown Westrick, Ludovic Patey, Reed Solomon","submitted_at":"2016-02-14T18:05:08Z","abstract_excerpt":"We answer a question posed by Hirschfeldt and Jockusch by showing that whenever $k > \\ell$, Ramsey's theorem for singletons and $k$-colorings, $\\mathsf{RT}^1_k$, is not strongly computably reducible to the stable Ramsey's theorem for $\\ell$-colorings, $\\mathsf{SRT}^2_\\ell$. Our proof actually establishes the following considerably stronger fact: given $k > \\ell$, there is a coloring $c : \\omega \\to k$ such that for every stable coloring $d : [\\omega]^2 \\to \\ell$ (computable from $c$ or not), there is an infinite homogeneous set $H$ for $d$ that computes no infinite homogeneous set for $c$. Thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04481","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"}