Authors: Raghavan, Dilip
Todorčević, Stevo 
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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