### 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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