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Suslin trees, the bounding number, and partition relations

2016/02/25 by Dilip Raghavan, Raghavan, Dilip, Stevo Todorcevic +1
Mathematics · #03E02 #03E17 #03E50 #03E55 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E02 #msc:03E17 #msc:03E50 #msc:03E55

paper · pdf · doi:10.48550/arxiv.1602.07901

17 pages, submitted

arxiv created 2016/02/25 · arxiv updated 2016/02/26

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+ \not→ ( κ+, logκ+) + 2 )2. The consistency of the positive partition relation \mathfrakb → (\mathfrakb, α)2 for all α< ω1 for the bounding number \mathfrakb is also established from large cardinals.

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