More on the Revised GCH and the Black Box

by Shelah. [Sh:829]
Annals Pure and Applied Logic, 2006
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.


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