The two-cardinal problem for languages of arbitrary cardinality

Abstract

Let ℒ be a first-order language of cardinality κ⁺⁺ with a distinguished unary predicate symbol U. In this paper we prove, working on L, the two cardinal transfer theorem (κ⁺,κ) ⇒ (κ⁺⁺,κ⁺) for this language. This problem was posed by Chang and Keisler more than twenty years ago.