A five element basis for the uncountable linear orders
Logic
2013-10-08 v1
Abstract
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.
Cite
@article{arxiv.math/0501525,
title = {A five element basis for the uncountable linear orders},
author = {Justin Tatch Moore},
journal= {arXiv preprint arXiv:math/0501525},
year = {2013}
}
Comments
21 pages