Realization of -types and Keisler’s order

We show that the analysis of Keisler’s order can be localized to the study of φ -types. Specifically, if D is a regular ultrafilter on λ such that l c f ( ω , D ) ≥ λ + and M is a model whose theory is countable, then M λ / D is λ + -saturated iff it realizes all φ -types of size λ .