The J-minimal sets in the hereditary theories

Abstract

Our attention in given article will be paid to the study of model-theoretic properties of hereditary Jonsson theories, while we consider Jonsson theories that retain jonsonness under any admissible enrichment. In given paper new concepts of "essential type", "essential geometric base" are introduced, the orbital types and strongly minimal sets within the framework of special subsets of the semantic model, on which a closure operator is given, defining the special geometry of Jonsson are considered. The results for the J-strongly minimal types of the semantic model in the case, when these sets are separated from the orbits of the central types of Jonsson hereditary theories are also obtained.