Pregeometry on the subsets of Jonsson theory’s semantic model

Abstract

One of the interesting achievements among investigations from modern model theory is the implement of local properties of the geometry of strongly minimal sets. In E. Hrushovski have proved remarkable results under this ideas and this one had impacted an essential infuence for development of methods and ideas of research for global properties of structures.These new model-theoretical features and approvals play an important role in E. Hrushovski’s proof of the Mordell–Lang Conjecture for function fields. In this article, we are trying to redefine the basic concepts of the above mentioned ideas on the formul subsets of some extentional-closed model for some fixed Jonsson theory. With the help of new concepts in the frame of Jonssoness features, pregeometry is given on all subsets of Jonsson theory’s semantic model. Minimal structures and, correspondingly, pregeometry and geometry of minimal structures are determined. We consider the concepts of dimension, independence, and basis in the Jonsson strongly minimal structures for Jonsson theories.