A five element basis for the uncountable linear orders

• Autores: Justin Tatch Moore
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 163, Nº 2, 2006, págs. 669-688
• Idioma: inglés
• DOI: 10.4007/annals.2006.163.669
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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, ¥ø1, ¥ø.1, C, C. where X is any suborder of the reals of cardinality .1 and C is any Countryman line. This confirms a longstanding conjecture of Shelah.