Abstract:
In this paper, the model-theoretical properties of the algebra of central types of mutually model-consistent
fragments are considered. Also, the connections between the center and the Jonsson theory in the permissible
signature enrichment are shown, and within the framework of such enrichment, instead of some complete
theory under consideration, we can obtain some complete 1-type, and we will call this type the central
type, while the theories under consideration will be hereditary. Our work is divided into 3 sections: 1) the
outer and inner worlds of the existentially closed model of the Jonsson theory (and the feature between
these worlds is considered for two existentially closed models of this theory); 2) the -comparison of two
existentially closed models (the Schroeder-Bernstein problem is adapted to the study of Jonsson theories in
the form of a JSB-problem); 3) an algebra of central types (we carry over the results of Section 2 for the
algebra (Fr(C); ), where C is the semantic model of the theory T). Also in this article, the following new
concepts have been introduced: the outer and inner worlds of one existentially closed model of the same
theory (as well as the world of this model), a totally model-consistent Jonsson theory. The main result of
our work shows that the properties of the algebra of Jonsson theories for the product of theories are used
as an application to the central types of fixed enrichment. And it is easy to see from the definitions of the
product of theories and hybrids that these concepts coincide if the product of two Jonsson theories gives a
Jonsson theory.
