On Robinson spectrum of the semantic Jonsson quasivariety of unars

Abstract

Given article is devoted to the study of semantic Jonsson quasivariety of universal unars of signature containing only unary functional symbol. The first section of the article consists of basic necessary concepts. There were defined new notions of semantic Jonsson quasivariety of Robinson unars JCU, its elementary theory and semantic model. In order to prove the main result of the article, there were considered Robinson spectrum RSp(JCU) and its partition onto equivalence classes [∆] by cosemanticness relation. The characteristic features of such equivalence classes [∆]∈RSp(JCU) were analysed. The main result is the following theorem of the existence of: characteristic for every class [∆] the meaning of which is Robinson theories of unars; class [∆] for any arbitrary characteristic; criteria of equivalence of two classes [∆]₁, [∆]₂. The obtained results can be useful for continuation of the various Jonsson algebras’ research, particularly semantic Jonsson quasivariety of S-acts over cyclic monoid.