{"paper":{"title":"The proof-theoretic strength of Ramsey's theorem for pairs and two colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Keita Yokoyama, Ludovic Patey","submitted_at":"2016-01-01T04:50:58Z","abstract_excerpt":"Ramsey's theorem for $n$-tuples and $k$-colors ($\\mathsf{RT}^n_k$) asserts that every k-coloring of $[\\mathbb{N}]^n$ admits an infinite monochromatic subset. We study the proof-theoretic strength of Ramsey's theorem for pairs and two colors, namely, the set of its $\\Pi^0_1$ consequences, and show that $\\mathsf{RT}^2_2$ is $\\Pi^0_3$ conservative over $\\mathsf{I}\\Sigma^0_1$. This strengthens the proof of Chong, Slaman and Yang that $\\mathsf{RT}^2_2$ does not imply $\\mathsf{I}\\Sigma^0_2$, and shows that $\\mathsf{RT}^2_2$ is finitistically reducible, in the sense of Simpson's partial realization o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00050","kind":"arxiv","version":4},"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"}