Forking in the category of existentially closed structures

Abstract

this paper, developing the theory of forking for the category of existentially closed models of an arbitrary universal theory T , assuming a suitable notion of "simplicity". Under the additional assumption that T has the amalgamation property (AP) and joint embedding property (JEP), Shelah did develop forking in some form. Hrushovski ([4]) rediscovered this latter class of theories (universal T with AP and JEP) calling them Robinson theories, and pointing out that all model-theoretic methods should apply to the category of e.c. models of such T . For Robinson theories, quantifier-free types are the main object of study, and as quantifier-free formulas are closed # Supported by NSF grant DMS-96-96268