{"paper":{"title":"Free sets for a set-mapping relative to a family of sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Antonio Avil\\'es, Claribet Pi\\~na","submitted_at":"2016-07-12T10:03:45Z","abstract_excerpt":"Given a family $\\mathcal{F}$ of subsets of $\\{1,\\ldots,m\\}$, we try to compute the least natural number $n$ such that for every function $S:[\\aleph_n]^{<\\omega}\\longrightarrow [\\aleph_n]^{<\\omega}$ there exists a bijection $u:\\{1,\\ldots,m\\}\\longrightarrow Y\\subset \\aleph_n$ such that $Su(A)\\cap Y \\subset u(A)$ for all $A\\in\\mathcal{F}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03291","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"}