Strong Covering Lemma and the G.C.H.

Abstract

We prove that e.g. contradicting the common assumption that for singular strong limit λ, 2^λ have a bound only when X has uncountable cofinality. We prove a strengthening of the covering lemma, not using the fine structure theory (only some well known consequences, see Theorem 0.2). We prove it essentially in all cases in which the covering lemma holds.