Les modèles dénombrables d’une théorie ayant des fonctions de Skolem
Daniel Lascar · Transactions of the American Mathematical Society · 1981
Let T T be a countable complete theory having Skolem functions. We prove that if all the types over finitely generated models are definable (this is the case for example if T T is stable), then either T T has 2 ℵ 0 {2^{{\aleph _0}}} countable models or all its models are homogeneous. The proof makes heavy use of stability techniques.