Forking and independence for fragments of Jonsson sets

Abstract

The concept of independence plays a very important role in Model Theory for classification of a fixed complete theory. In this paper, we study the Jonsson theories, which, generally speaking, are not complete. For such theories, the concept of forking is introduced axiomatically in the framework of the study of the Jonsson subsets of the semantic model of this theory. Equivalence of forking by Shelah, by Laskar-Poizat and an axiomatically given forking for existential types over subsets of the semantic model of the Jonsson theory is given. Further, as and for complete theories, independence is defined through the notion of non-forking.