A five element basis for the uncountable linear orders
成果类型：
Article
署名作者：
Moore, Justin Tatch
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2006.163.669
发表日期：
2006
页码：
669-688
关键词：
摘要：
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, w(1), w(2), C, C* where X is any suborder of the reals of cardinality N-1 and C is any Countryman line. This confirms a longstanding conjecture of Shelah.