# Sh:861

- Shelah, S. (2007).
*Power set modulo small, the singular of uncountable cofinality*. J. Symbolic Logic,**72**(1), 226–242. arXiv: math/0612243 DOI: 10.2178/jsl/1174668393 MR: 2298480 -
Abstract:

Let \mu be singular of uncountable cofinality. If \mu> 2^{{\rm cf}(\mu)}, we prove that in {\mathbb P}=([\mu]^\mu, \supseteq) as a forcing notion we have a natural complete embedding of {\rm Levy}(\aleph_0,\mu^+) (so {\mathbb P} collapses \mu^+ to \aleph_0) and even {\rm Levy}(\aleph_0, {\bf U}_{J^{{\rm bd}}_\kappa}(\mu)). The “natural" means that the forcing (\{p \in [\mu]^\mu:p closed\},\supseteq) is naturally embedded and is equivalent to the Levy algebra. If \mu<2^{{\rm cf}(\mu)} we have weaker results. - Version 2019-05-08_11 (22p) published version (18p)

Bib entry

@article{Sh:861, author = {Shelah, Saharon}, title = {{Power set modulo small, the singular of uncountable cofinality}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {72}, number = {1}, year = {2007}, pages = {226--242}, issn = {0022-4812}, mrnumber = {2298480}, mrclass = {03E04 (03E05 03E40)}, doi = {10.2178/jsl/1174668393}, note = {\href{https://arxiv.org/abs/math/0612243}{arXiv: math/0612243}}, arxiv_number = {math/0612243} }