{"paper":{"title":"Separating principles below Ramsey's Theorem for Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Henry Towsner, Manuel Lerman, Reed Solomon","submitted_at":"2013-02-04T20:37:08Z","abstract_excerpt":"In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from $\\RT$, Ramsey's Theorem for Pairs. These principles tend to fall outside of the \"big five\" systems of reverse mathematics and a complicated picture of subsystems below $\\RT$ has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that $\\ADS$ is not equivalent to $\\CAC$ and that $\\EM$ is not equivalent to $\\RT$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0828","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"}