### 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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