Abstract
We prove that, e.g., if μ > cf(μ) = N0 and μ > 2N0 and every stationary family of countable subsets of μ+ reflects in some subset of μ+ of cardinality N1, then the SCH for μ+ holds (moreover, for μ+, any scale for μ+ has a bad stationary set of cofinality N1). This answers a question of Foreman and Todorčević who get such a conclusion from the simultaneous reflection of four stationary sets.
Original language | English |
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Pages (from-to) | 95-111 |
Number of pages | 17 |
Journal | Fundamenta Mathematicae |
Volume | 198 |
Issue number | 2 |
DOIs | |
State | Published - 2008 |
Keywords
- Pcf
- Reflection
- Set theory
- Singular cardinal hypothesis
- Stationary sets