Similarities of Jonsson spectra’s classes
Йонсондық спектрлердiң кластарының ұқсастықтары
Подобия классов йонсоновских спектров
Yeshkeyev A.R. Ulbrikht O.I. Urken G.A.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#112Issue 4130 - 143 pp.
The study of syntactic and semantic properties of a first-order language, generally speaking, for incomplete theories, is one of the urgent problems of mathematical logic. In this article we study Jonsson theories, which are satisfied by most classical examples from algebra and which, generally speaking, are not complete. A new and relevant method for studying Jonson theories is to study these theories using the concepts of syntactic and semantic similarities. The most invariant concept is the concept of syntactic similarity of theories, because it preserves all the properties of the theories under consideration. The main result of this article is the fact that any perfect Jonson theory which are complete for existential sentences, is syntactically similar to some polygon theory (S-polygon, where S is a monoid). This result extends to the corresponding classes of Jonsson theories from the Jonsson spectrum of an arbitrary model of an arbitrary signature.
cosemanticness , Jonsson spectrum , Jonsson theory , perfectness , S-act , semantic model , semantic similarities , syntactic
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Karaganda Buketov University Institute of Applied Mathematics, Karaganda, Kazakhstan
Karaganda Buketov University Institute of Applied Mathematics
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