Model-theoretic properties of semantic pairs and e.f.c.p. in Jonsson spectrum

Abstract

The article is committed to the study of model-theoretic properties of stable hereditary Jonsson theories, wherein we consider Jonsson theories that retain jonssonnes for any permissible enrichment. The paper proves a generalization of stability that relates stability and classical stability for Jonsson spectrum. This paper introduces new concepts such as “existentially finite cover property” and “semantic pair”. The basic properties of e.f.c.p. and semantic pairs in the class of stable perfect Jonsson spectrum are studied.