|Title:||Suslin trees, the bounding number, and partition relations||Journal:||Israel Journal of Mathematics||Volume:||225||Issue:||2||First page:||771||Last page:||796||Issue Date:||18-Apr-2018||Rank:||M22||ISSN:||0021-2172||DOI:||10.1007/s11856-018-1677-1||Abstract:||
We investigate the unbalanced ordinary partition relations of the form λ → (λ, α)2 for various values of the cardinal λ and the ordinal α. For example, we show that for every infinite cardinal κ, the existence of a κ+-Suslin tree implies κ+ ↛ (κ+, logκ(κ+) + 2)2. The consistency of the positive partition relation b → (b, α)2 for all α < ω1 for the bounding number b is also established from large cardinals.
|Publisher:||Springer Link||Project:||National University of Singapore, Grant no. R-146-000-211-112.
NSERC, Grant no. 201598
CNRS, Grant no. IMJ-PRG UMR7586
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