Reflection implies the SCH

• Autorzy: Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

We prove that, e.g., if μ > cf(μ) = ℵ₀ and $μ > 2^{ℵ₀}$ 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.

Kategorie tematyczne

• 03E04: Ordered sets and their cofinalities; pcf theory
• 03E05: Other combinatorial set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 198
• Numer: 2
• Strony: 95-111

Daty

wydano

2008

Twórcy

autor

Saharon Shelah

• Institute of Mathematics, The Hebrew University, Jerusalem, Israel
• Mathematics Department, Rutgers University, New Brunswick, NJ 08854, U.S.A.

Identyfikatory

DOI

10.4064/fm198-2-1