When 𝑈(𝜅) can be mapped onto 𝑈(𝜔)

Abstract

U ( κ ) U(\kappa ) can be mapped onto U ( ω ) iff cf ( κ ) = ω or κ ⩾ 2 ω . U(\omega ){\text {iff}}\;{\text {cf}}(\kappa ) = \omega {\text {or}}\kappa \geqslant {2^\omega }. .