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 ¾essential type¿, ¾essential 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.

Keywords

• Jonsson theory
• semantic mode
• hereditary theory
• J-minimal set
• J-strongly minimal set
• permissible enrichment