arXiv math/04043232004-04math.LO

Reflection implies the SCH

Saharon Shelah

发表信息：: Fund. Math. 198 No. 2 (2008) 95--111

英文摘要：

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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