More on: the revised GCH and middle diamond

Abstract

We strengthen the revised GCH theorem by showing, e.g., that for lambda=cf(lambda)>beth_omega, for all but finitely many regular kappa<beth_omega, lambda is accessible on cofinality kappa in a weak version of it holds. In particular, lambda=2^mu=mu^+>beth_omega implies the diamond on lambda is restricted to cofinality kappa for all but finitely many kappa in Reg cap beth_omega and we strengthen the results on the middle diamond. Moreover, we get stronger results on the middle diamond.