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arXiv:math/0501525 [math.LO]AbstractReferencesReviewsResources

A five element basis for the uncountable linear orders

Justin Tatch Moore

Published 2005-01-28Version 1

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.

Comments: 21 pages
Journal: Ann. of Math. (2) 163 (2006), no. 2, 669--688
Categories: math.LO
Subjects: 03E35, 03E75, 06A05, 03E02
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