# Sh:829

• Shelah, S. (2006). More on the revised GCH and the black box. Ann. Pure Appl. Logic, 140(1-3), 133–160.
• Abstract:
We strengthen the revised GCH theorem by showing, e.g., that for \lambda={\rm 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{\rm Reg}\cap \beth_\omega and we strengthen the results on the middle diamond. Moreover, we get stronger results on the middle diamond.
• published version (28p)
Bib entry
@article{Sh:829,
author = {Shelah, Saharon},
title = {{More on the revised GCH and the black box}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {140},
number = {1-3},
year = {2006},
pages = {133--160},
issn = {0168-0072},
mrnumber = {2224056},
mrclass = {03E50 (03E04 03E05 03E10)},
doi = {10.1016/j.apal.2005.09.013},
note = {\href{https://arxiv.org/abs/math/0406482}{arXiv: math/0406482}},
arxiv_number = {math/0406482}
}