Meeting numbers and pseudopowers

Mathematical Logic Quarterly 67 (1):59-76 (2021)
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Abstract

We study the role of meeting numbers in pcf theory. In particular, Shelah's Strong Hypothesis is shown to be equivalent to the assertion that for any singular cardinal σ of cofinality ω, there is a size collection Q of countable subsets of σ with the property that for any infinite subset a of σ, there is a member of Q meeting a in an infinite set.

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10.1002/malq.201900039

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References found in this work

Shelah's pcf theory and its applications.Maxim R. Burke & Menachem Magidor - 1990 - Annals of Pure and Applied Logic 50 (3):207-254.
Scales with various kinds of good points.Pierre Matet - 2018 - Mathematical Logic Quarterly 64 (4-5):349-370.
A relative of the approachability ideal, diamond and non-saturation.Assaf Rinot - 2010 - Journal of Symbolic Logic 75 (3):1035-1065.
Two‐cardinal diamond star.Pierre Matet - 2014 - Mathematical Logic Quarterly 60 (4-5):246-265.
Guessing more sets.Pierre Matet - 2015 - Annals of Pure and Applied Logic 166 (10):953-990.

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