Shelah's pcf theory and its applications



Title Shelah's pcf theory and its applications
Author(s) Maxim R. Burke, M. Magidor
Journal Annals of Pure and Applied Logic
Date 1990
Volume 50
Issue 3
Start page 207
End page 254
Abstract This is a survey paper giving a self-contained account of Shelah's theory of the pcf function pcf(a) = {cf(PI a/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.

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