Bounding the consistency strength of a five element linear basis

@inproceedings{Knig2008BoundingTC,
  title={Bounding the consistency strength of a five element linear basis},
  author={Bernhard K{\"o}nig and Paul B. Larson and Justin Tatch Moore and Boban Velickovic},
  year={2008}
}
In [13] it was 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 proof have consistency strength of at least infinitely many Woodin cardinals. In this paper 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 L. A crucial notion in the proof is the saturation of an… CONTINUE READING
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