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Reflection implies the SCH

Saharon Shelah
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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.

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Saharon Shelah. 2007-09-30. Reflection implies the SCH. https://arxiv.org/abs/math/0404323

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