On some types of algebras of a Jonsson spectrum

We work in the framework of study of Jonsson spectra for concerning classes of structures. In this paper, the issues of cosemantic Jonsson theories and Jonsson spectrum are discussed. There are shown some results on the opportunity of introducing some types of algebras on the Jonsson spectrum. Also, it is proved that the finite axiomatizability of the Kaiser hull of the Jonsson theory implies the finiteness of cosemantic Jonsson theories.