Reflection implies the SCH
Logic
2007-09-30 v2
Abstract
We prove that, e.g., if mu >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.
Cite
@article{arxiv.math/0404323,
title = {Reflection implies the SCH},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/0404323},
year = {2007}
}