{"paper":{"title":"The reverse mathematics of Hindman's theorem for sums of exactly two elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barbara F. Csima, Carl G. Jockusch, Damir D. Dzhafarov, Denis R. Hirschfeldt, Jr., Linda Brown Westrick, Reed Solomon","submitted_at":"2018-04-25T21:40:25Z","abstract_excerpt":"Hindman's Theorem (HT) states that for every coloring of $\\mathbb N$ with finitely many colors, there is an infinite set $H \\subseteq \\mathbb N$ such that all nonempty sums of distinct elements of $H$ have the same color. The investigation of restricted versions of HT from the computability-theoretic and reverse-mathematical perspectives has been a productive line of research recently. In particular, HT$^{\\leqslant n}_k$ is the restriction of HT to sums of at most $n$ many elements, with at most $k$ colors allowed, and HT$^{=n}_k$ is the restriction of HT to sums of \\emph{exactly} $n$ many ele"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09809","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"}