On Kaiser class of unars in expanded signature

Abstract

The present paper is connected with studying properties of Jonsson theories of a unar. The main idea is to study a structure of the signature with one unary functional symbol by expanding it with both a new constant symbol and a unary predicate symbol. We construct the semantic Jonsson quasivariety using the semantic models of enriched Jonsson primitives of unars and consider its Jonsson spectrum, divided by cosemanticness relation onto factor-set, and the obtained factor-set is divided by a new equivalence relation with regard to the Kaiser class. Additionally, we consider the notion of normal Jonsson theory and prove that the theory of all unars is normal, and obtain new results concerning components of unars and the Kaiser class of their theories.