Existentially positive Mustafin theories of S-acts over a group
Группалар маңайындағы полигондардың экцистенциалды позитивтi мұстафиндiк теориясы
Экзистенциально позитивные мустафинские теории полигонов над группой
Yeshkeyev A.R. Ulbrikht O.I. Yarullina A.R.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#106Issue 2172 - 185 pp.
The paper is connected with the study of Jonsson spectrum notion of the fixed class of models of S-acts signature, assuming a group as a monoid of S-acts. The Jonsson spectrum notion is effective when describing theoretical-model properties of algebras classes whose theories admit joint embedding and amalgam properties. It is usually sufficient to consider universal-existential sentences true on models of this class. Up to the present paper, the Jonsson spectrum has tended to deal only with Jonsson theories. The authors of this study define the positive Jonsson spectrum notion, the elements of which can be, non-Jonsson theories. This happens because in the definition of the existentially positive Mustafin theories considered in a given paper involve not only isomorphic embeddings, but also immersions. In this connection, immersions are considered in the definition of amalgam and joint embedding properties. The resulting theories do not necessarily have to be Jonsson. We can observe that the above approach to the Jonsson spectrum study proves to be justified because even in the case of a non-Jonsson theory there exists regular method for finding such Jonsson theory that satisfies previously known notions and results, but that will also be directly related to the existentially positive Mustafin theory in question.
cosemanticity , immersion , Jonsson S-acts theory , Jonsson spectrum , Jonsson theory , perfect Jonsson theory , positive Jonsson theory , positive model theory , S-acts , ∃PM-theory
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Karagandy University of the name of academician E.A. Buketov, Karaganda, Kazakhstan
Karagandy University of the name of academician E.A. Buketov
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