{"paper":{"title":"Generalized low solution of $\\mathsf{RT}_k^1$ problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Lu Liu","submitted_at":"2016-02-19T17:29:15Z","abstract_excerpt":"We study the \"coding power\" of an arbitrary $\\mathsf{RT}_k^1$-instance. We prove that every $\\mathsf{RT}_k^1$-instance admit non trivial generalized low solution. This is somewhat related to a problem proposed by Patey. We also answer a question proposed by Liu, i.e., we prove that there exists a $\\mathbf{0}'$-computable $\\mathsf{RT}_3^1$-instance, $I_3^1$, such that every $\\mathsf{RT}_2^1$-instance admit a non trivial solution that does not compute any non trivial solution of $I_3^1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06232","kind":"arxiv","version":2},"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"}