Bounding the consistency strength of a five element linear basis
by
Justin Tatch Moore
Boise State University
Coauthors: Bernhard Koenig, Paul Larson, Boban Velickovic

It has been demonstrated that the Proper Forcing Axiom implies that there is a five element basis for the class of uncountable linear orders. The assumptions needed in the original proof have consistency strength of at least infinitely many Woodin cardinals. We reduce the upper bound on the consistency strength of such a basis to something less than a Mahlo cardinal, a hypothesis which can hold in the constructible universe. A crucial notion in the proof is the saturation of an Aronszajn tree, a statement which may be of broader interest.

Date received: February 27, 2006