{"paper":{"title":"Possible pcf algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Saharon Shelah, Thomas Jech","submitted_at":"1994-12-03T00:00:00Z","abstract_excerpt":"There exists a family $\\{B_{\\alpha}\\}_{\\alpha<\\omega_1}$ of sets of countable ordinals such that\n o $\\max B_{\\alpha}=\\alpha$,\n o if $\\alpha\\in B_{\\beta}$ then $B_{\\alpha}\\subseteq B_{\\beta}$,\n o if $\\lambda\\leq \\alpha$ and $\\lambda$ is a limit ordinal then $B_{\\alpha}\\cap\\lambda$ is not in the ideal generated by the $B_{\\beta}$, $\\beta<\\alpha$, and by the bounded subsets of $\\lambda$,\n o there is a partition $\\{A_n\\}_{n=0}^{\\infty}$ of $\\omega_1$ such that for every $\\alpha$ and every $n,$ $B_{\\alpha}\\cap A_n$ is finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9412208","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"}