English

Knaster and friends II: The C-sequence number

Logic 2019-12-10 v1

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 U(...), introduced in Part I of this series.

Cite

@article{arxiv.1912.03342,
  title  = {Knaster and friends II: The C-sequence number},
  author = {Chris Lambie-Hanson and Assaf Rinot},
  journal= {arXiv preprint arXiv:1912.03342},
  year   = {2019}
}
R2 v1 2026-06-23T12:38:33.316Z