Moti Gitik, Ralf Schindler, and Saharon Shelah PCF theory and Woodin cardinals

Cardinal arithmetic deals with possible behaviours of the function Easton, inventing a class version of Cohen’s

set forcing (cf. [4]) had shown that if Reg then there is a forcing

Reg. (Here, Card denotes the class of all infinite cardinals, and Reg denotes the class of all infinite regular cardinals.) However, in any of Easton’s models, the so-called Singular Cardinal Hypothesis (abbreviated by SCH) holds true (cf. [14, Exercise 20.7]),

for all infinite cardinals κ. If SCH holds then cardinal arithmetic is in some sense simple, cf. [14, Lemma 8.1].