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.
"The two-cardinal problem for languages of arbitrary cardinality." J. Symbolic Logic 75 (3) 785 - 801, September 2010. https://doi.org/10.2178/jsl/1278682200