{"paper":{"title":"A five element basis for the uncountable linear orders","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Justin Tatch Moore","submitted_at":"2005-01-28T22:39:46Z","abstract_excerpt":"In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows from the Proper Forcing Axiom, a strong form of the Baire Category Theorem. The elements are X, omega_1, omega_1^*, C, C^* where X is any suborder of the reals of cardinality aleph_1 and C is any Countryman line. This confirms a longstanding conjecture of Shelah."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501525","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"}