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Reflection implies the SCH

Saharon Shelah (2008)

Fundamenta Mathematicae

We prove that, e.g., if μ > cf(μ) = ℵ₀ and μ > 2 and every stationary family of countable subsets of μ⁺ reflects in some subset of μ⁺ of cardinality ℵ₁, then the SCH for μ⁺ holds (moreover, for μ⁺, any scale for μ⁺ has a bad stationary set of cofinality ℵ₁). This answers a question of Foreman and Todorčević who get such a conclusion from the simultaneous reflection of four stationary sets.

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