Properties of lattices of the existential formulas of Jonsson fragments

Abstract

This article is devoted to studying of the properties of model-theoretic concepts of a fragment of the Jonsson sets and their application to the lattices of existential formulas. The concept of the Jonsson set allocates as a special subset of the semantic models for the considered the Jonsson theory. Next, we present some model-theoretic properties of the fragments of the considered Jonsson sets that were previously considered for the Jonsson theories. These properties describe the relationship between the lattices of the existential formulas and a center of the considered fragment.