Forcing companions of Jonsson AP-theories

This article is devoted to the study of the forcing companions of the Jonsson AP-theories in the enriched signature. It is proved that the forcing companion of the theory does not change when expanding the theories under consideration, which have some properties, by adding new predicate and constant symbols to the language. The model-theoretic results obtained in this paper in general form are supported by examples from differential algebra. An approach in combining a Jonsson and non-Jonsson theories is demonstrated. In this paper, for the first time in the history of Model Theory. This will allow us to further develop the methods of research of Jonsson theories and expand the apparatus for studying incomplete theories.