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Meeting numbers and pseudopowers
Author(s) -
Matet Pierre
Publication year - 2021
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201900039
Subject(s) - cofinality , mathematics , countable set , assertion , property (philosophy) , set (abstract data type) , infinite set , discrete mathematics , pure mathematics , uncountable set , epistemology , computer science , philosophy , programming language
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 σ + 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.