Reflection implies the SCH

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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 languageEnglish
Pages (from-to)95-111
Number of pages17
JournalFundamenta Mathematicae
Volume198
Issue number2
DOIs
StatePublished - 2008

Keywords

  • Pcf
  • Reflection
  • Set theory
  • Singular cardinal hypothesis
  • Stationary sets

Fingerprint

Dive into the research topics of 'Reflection implies the SCH'. Together they form a unique fingerprint.

Cite this