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Suslin trees, the bounding number, and partition relations

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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+, log κ (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.

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Authors and Affiliations

  1. Department of Mathematics National University of Singapore, Singapore, 119076, Singapore

    Dilip Raghavan

  2. Dpartment of Mathematics, University of Toronto, Toronto, M5S 2E4, Canada

    Stevo Todorcevic

  3. Institut de Mathématique de Jussieu, UMR 7586, Case 247, 4 place Jussieu, 75252, Paris Cedex, France

    Stevo Todorcevic

Authors
  1. Dilip Raghavan
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  2. Stevo Todorcevic
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Corresponding author

Correspondence to Dilip Raghavan.

Additional information

Partially supported by National University of Singapore research grant number R-146-000-211-112.

Partially supported by grants from NSERC (201598) and CNRS (IMJ-PRG UMR7586).

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Raghavan, D., Todorcevic, S. Suslin trees, the bounding number, and partition relations. Isr. J. Math. 225, 771–796 (2018). https://doi.org/10.1007/s11856-018-1677-1

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  • DOI: https://doi.org/10.1007/s11856-018-1677-1

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