Many partition relations below density |
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Authors: | Saharon Shelah |
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Institution: | 1.Einstein Institute of Mathematics, Edmond J. Safra Campus,The Hebrew University of Jerusalem,Givat Ram, Jerusalem,Israel;2.Department of Mathematics, Hill Center — Busch Campus Rutgers,The State University of New Jersey,Piscataway,USA |
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Abstract: | We force 2 λ to be large, and for many pairs in the interval (λ, 2 λ ) a strong version of the polarized partition relations holds. We apply this to problems in general topology. For example, consistently, every 2 λ is the successor of a singular and for every Hausdorff regular space X, hd(X) ≤ s(X)+3, hL(X) ≤ s(X)+3 and better when s(X) is regular, via a halfgraph partition relations. For the case s(X) = ℵ 0 we get hd(X), hL(X) ≤ N 2. |
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