Reflection implies the SCH

by Shelah. [Sh:794]
Fundamenta Math, 2008
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.


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