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This work is related to the concepts of admissibility, interpretability, syntactic similarity and semantic similarity of Jonsson’s theories.This new concept generalize the notion of syntactic and semantic similarities for Jonsson theories. In the frame of study of preservation of the definable formulas subsets of Jonsson theory’s semantic model regarding to considering morphisms the concepts of admissibility, interpretability, domination and similarity play a very important role. As an example, we consider the theory of Boolean algebras. These concepts are closely related to the concept of admissibility by one theory on the other. The interest of this paper is that the examples examined show the fact that admissibility, interpretability and similarity can be considered on algebras of different signatures.In this work the main definitions of notions and the basic directions of further researches are studied.

The admissibility and similarity of Jonsson theories