About central types and the cosemanticness of the ∆-PM fragment of the Jonsson set

Abstract

This article is concerned with the enrichment of the signature. In own time, when studying the stability of the theory and the concept of an elementary pair of models, Mustafin T.G. had noticed that these things are related to each other and he introduced the concept T ^∗-stability [1]. In fact, some enrichment of the signature is considered. Generally speaking, the theories obtained in the extended language are incomplete, therefore, the number of such completions of these theories is sought. This number also determines stability in the sense of T ^∗-stability. It was noted by E.A.Palyutin in [2] that the concept of T ^∗-stability is not invariant with respect to definability of type. But we know that in the classical sense of S.Sellach the stability of the theory is invariant with respect to the definability of type. Therefore Palyutin E.A. had introduced the concept E ^∗-stability, which preserved the definability of type...