Knaster and friends II: The C-sequence number

Joint work with Chris Lambie-Hanson.

Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic,
we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable cardinal. We prove a number of ZFC and independence results about the C-sequence number and its relationship with large cardinals, stationary reflection, and square principles.
We then introduce and study the more general C-sequence spectrum and uncover some tight
connections between the C-sequence spectrum and the strong coloring principle introduced in Part I of this series.

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Citation information:

C. Lambie-Hanson and A. Rinot, Knaster and friends II: The C-sequence number, J. Math. Logic, 21(1): 2150002, 54pp, 2021.