The Properties of Similarity for Jonsson’s Theories and Their Models
Keywords:
Jonsson theory, semantic model, companion, model completeness, syntactic and semantic similarities, atomic and algebraically prime models, existentially closed model, lattice of existential formulasAbstract
Actually, we study the connections of the ∆-PJ-theories with their centers. The properties of various companions of some ∆-PJ-theories and their connection with this theory are considered. Also the similarity of the central types of ∆-PJ-theories in the enriched language is considered. In the class of perfect ∆-PJ-theories the conditions of coincidence of algebraic primeness with some sort of atomic models are found. In the class of ∆-PJ-theories, the concepts of syntactic and semantic similarities are introduced and the results on the relationship of these similarities in this class with their centers are obtained.
