The search for trivial types

Abstract

In this paper, we look at strongly minimal sets definable in a differentially closed field of characteristic 0. In [3], Hrushovski and Sokolović show that such sets are essentially Zariski geometries. Thus either thre is a definable strongly minimal field nonorthogonal to $D$, or $D$ is locally modular and nontrivial, or $D$ is trivial. We show that the strongly minimal sets defined by a certain family of differential equations are trivial. We also prove a theorem wich provides a test for the orthogonality of types over an ordinary differential field.