My question is regarding model-theoretic forcing developed by Robinson.
I understand that model-theoretic forcing is useful in the study of existentially closed models, such as constructing e.c. models and calculating resultants of quantifier-free formulas in groups.
Can it be used to study other aspects of e.c. models? In particular, can it be used to show that a finite subset $T'$ of $T^*$, the model-completion of a universal theory $T$, does not axiomatize $T^*$? Here, I would imagine that one constructs a non-e. c. model satisfying $T'$.
I'm trying to read Hodges's Building Models by Games, but I thought that I should learn if the subject of the book is relevant to the said question that I had in mind.