Reflection implies the SCH
Abstract
We prove that, e.g., if mu >cf(mu)= aleph0 and mu>2aleph0 and every stationary family of countable subsets of mu+ reflect in some subset of mu+ of cardinality aleph1, then the SCH for mu+ (moreover, for mu+, any scale for mu+ has a bad stationary set of cofinality aleph1). This answers a question of Foreman and Todorcevic who got such conclusion from the simultaneous reflection of four stationary sets.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.