Journal of Mathematical Logic 21 (1):2150002 (2020)

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
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Reprint years 2021
DOI 10.1142/s0219061321500021
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References found in this work BETA

Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
Simultaneous Stationary Reflection and Square Sequences.Yair Hayut & Chris Lambie-Hanson - 2017 - Journal of Mathematical Logic 17 (2):1750010.
Saturated Ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
Chain Conditions of Products, and Weakly Compact Cardinals.Assaf Rinot - 2014 - Bulletin of Symbolic Logic 20 (3):293-314,.

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