{"paper":{"title":"A dichotomy on Schreier sets","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Robert Judd","submitted_at":"1997-06-05T00:00:00Z","abstract_excerpt":"We show that the Schreier sets $\\mathcal{S}_{\\alpha}\\ (\\alpha<\\omega_1)$ satisfy the following dichotomy property. For every hereditary collection $\\cf$ of finite subsets of $\\N$, either there exists infinite $M=(m_i)_1^{\\infty}\\subseteq\\N$ such that $\\cs_{\\alpha}(M)=\\{\\{m_i:i\\in E\\}:E\\in\\cs_{\\alpha}\\}\\subseteq\\cf$, or there exist infinite $M=(m_i)_1^{\\infty},N\\subseteq\\N$ such that $\\cf[N](M)=\\{\\{m_i:i\\in F\\}:F\\in\\cf \\mbox{ and } F\\subset N\\}\\subseteq\\cs_{\\alpha}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9706209","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"}