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)

@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}
}