# Sh:829

- Shelah, S. (2006).
*More on the revised GCH and the black box*. Ann. Pure Appl. Logic,**140**(1-3), 133–160. arXiv: math/0406482 DOI: 10.1016/j.apal.2005.09.013 MR: 2224056 -
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. - Version 2006-02-16_11 (43p) 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} }