Fundamentals of forking (Q1074574)

The paper gives a self-contained exposition of the fundamental facts of Shelah's stability theory concerning the notion of forking. The emphasis is on giving as short and direct proofs as possible of the basic properties and equivalences between the various definitions of forking. The framework of the study is broad enough to incorporate the benefits of Shelah's \(T^{eq}\). The approach allows to prove a generalization of Lachlan's normalization theorem. Everywhere the authors point out a minimum of stability assumptions needed for a smooth theory of forking. The paper is intended to serve as an introduction for readers familiar with general model theory who wish to study the literature on stability theory.