{"paper":{"title":"On $\\left( 1,\\omega_{1}\\right) $\\emph{-}weakly universal functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Osvaldo Guzman","submitted_at":"2018-10-22T03:36:47Z","abstract_excerpt":"A function $U:\\left[ \\omega_{1}\\right] ^{2}\\longrightarrow\\omega$ is called $\\left( 1,\\omega_{1}\\right) $\\emph{-weakly universal }if for every function $F:\\left[ \\omega_{1}\\right] ^{2}\\longrightarrow\\omega$ there is an injective function $h:\\omega_{1}\\longrightarrow\\omega_{1}$ and a function $e:\\omega \\longrightarrow\\omega$ such that $F\\left( \\alpha,\\beta\\right) =e\\left( U\\left( h\\left( \\alpha\\right) ,h\\left( \\beta\\right) \\right) \\right) $ for every $\\alpha,\\beta\\in\\omega_{1}$. We will prove that it is consistent that there are no $\\left( 1,\\omega_{1}\\right) $\\emph{-}weakly universal functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09072","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"}