Strong Splitting in Stable Homogeneous Models

Abstract In this paper we study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in Hyttinen (Fund. Math. 156 (1998) 167–182). We apply this to prove a structure theorem. We also show that dop and sdop are essentially equivalent, where the negation of dop is the property we use in our structure theorem and sdop implies nonstructure, see Hyttinen (1998).