{"paper":{"title":"Free Boolean algebras over unions of two well orderings","license":"","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Latifa Faouzi, Robert Bonnet, Wies{\\l}aw Kubi\\'s","submitted_at":"2007-05-13T10:32:04Z","abstract_excerpt":"Given a partially ordered set $P$ there exists the most general Boolean algebra $F(P)$ which contains $P$ as a generating set, called the {\\it free Boolean algebra} over $P$. We study free Boolean algebras over posets of the form $P=P_0\\cup P_1$, where $P_0,P_1$ are well orderings. We call them {\\it nearly ordinal algebras}.\n  Answering a question of Maurice Pouzet, we show that for every uncountable cardinal $\\kappa$ there are $2^\\kappa$ pairwise non-isomorphic nearly ordinal algebras of cardinality $\\kappa$.\n  Topologically, free Boolean algebras over posets correspond to compact 0-dimension"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.1824","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"}