is only one of the consequences of pcf theory.
While Jack Silver proved that GCH below a
singular cardinal of uncountable
cofinality implies GCH AT that cardinal, Menachem Magidor proved that
GCH below aleph_omega does not prove GCH at aleph_omega.
pcf theory, as developed in Shelah's book "Cardinal Arithmetic", was developed not only to compute or estimate the values of the gimel function kappa^(cf(kappa) [from which one can then compute arbitrary powers kappa^lambda], but rather to analyse the order-theoretic structure of products kappa^(cf(kappa)) for singluar cardinals kappa, or more generally , of products of the form product_i lambda_i , where (lambda_i: i < delta) is a short sequence of regular cardinals.
The table of contents for the "Cardinal arithmetic" book, together with the introduction, is available as a DVI file.