Reflection Implies the Sch Sh794

Abstract

We prove that, e.g., if μ > cf(μ) = א0 and μ > 20 and every stationary family of countable subsets of μ reflect 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 gets such conclusion from the simultaneous… (More)

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