Many partition relations below density

Details Many partition relations below density Many partition relations below density

2009-02-03

arxiv.org/abs/0902.0440v2

Mathematics

Logic

Scientific paper

We force 2^lambda to be large and for many pairs in the interval (lambda,2^lambda) a stronger version of the polarized partition relations hold. We apply this to problems in general topology. E.g. consistently, every 2^lambda is successor of singular and for every Hausdorff regular space X, hd(X) <= s(X)^{+3}, hL(X) <= s(X)^{+3} and better for s(X) regular, via a half-graph partition relation. For the case s(X)=aleph_0 we get hd(X), hL(X) <=aleph_2.

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