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^+ holds. (Moreover, for \mu^+, any scale for \mu^+ has a bad stationary set of cofinality \aleph_1.) This answers a question of Foreman and Todorčević, who got such conclusion from the simultaneous reflection of four stationary sets.
• Version 2007-10-01_10 (20p) published version (17p)

@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},
 mrnumber = {2369124},
 mrclass = {03E04 (03E05)},
 doi = {10.4064/fm198-2-1},
 note = {\href{https://arxiv.org/abs/math/0404323}{arXiv: math/0404323}},
 arxiv_number = {math/0404323}
}