  This paper deals with the class of existentially closed models of fields with
a distinguished submodule (over a fixed subring). In the positive
characteristic case, this class is elementary and was investigated by the
first-named author. Here we study this class in Robinson's logic, meaning the
category of existentially closed models with embeddings following Haykazyan and
Kirby, and prove that in this context this class is NSOP$_1$ and TP$_2$.
