# Sh:794

- Shelah, S. (2008).
*Reflection implies the SCH*. Fund. Math.,**198**(2), 95–111. arXiv: math/0404323 DOI: 10.4064/fm198-2-1 MR: 2369124 -
Abstract:

We prove that, e.g., if \mu>{\rm cf}(\mu)=\aleph_0 and \mu> 2^{\aleph_0} and every stationary family of countable subsets of \mu^+ reflect in some subset of \mu^+ of cardinality \aleph_1, then the SCH for \mu^+ (moreover, for \mu^+, any scale for \mu^+ has a bad stationary set of cofinality \aleph_1). This answers a question of Foreman and Todorcevic who got such conclusion from the simultaneous reflection of four stationary sets. - published version (17p)

Bib entry

@article{Sh:794, author = {Shelah, Saharon}, title = {{Reflection implies the SCH}}, journal = {Fund. Math.}, fjournal = {Fundamenta Mathematicae}, volume = {198}, number = {2}, year = {2008}, pages = {95--111}, issn = {0016-2736}, doi = {10.4064/fm198-2-1}, mrclass = {03E04 (03E05)}, mrnumber = {2369124}, mrreviewer = {Paul Bradley Larson}, doi = {10.4064/fm198-2-1}, note = {\href{https://arxiv.org/abs/math/0404323}{arXiv: math/0404323}}, arxiv_number = {math/0404323} }