Shelah's pcf theory and its applications

Maxim R. Burke; Menachem Magidor

doi:10.1016/0168-0072(90)90057-9

Shelah's pcf theory and its applications

Maxim R. Burke^*, Menachem Magidor

^*Corresponding author for this work

Einstein Institute of Mathematics

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Abstract

This is a survey paper giving a self-contained account of Shelah's theory of the pcf function pcf(a)={cf(Πa/D, <_D):D is an ultrafilter on a}, where a is a set of regular cardinals such that |a|<min(a). We also give several applications of the theory to cardinal arithmetic, the existence of Jonsson algebras, and partition calculus.

Original language	English
Pages (from-to)	207-254
Number of pages	48
Journal	Annals of Pure and Applied Logic
Volume	50
Issue number	3
DOIs	https://doi.org/10.1016/0168-0072(90)90057-9
State	Published - 14 Dec 1990

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Shelah's pcf theory and its applications

Abstract

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