Model companion properties of some theories
Кейбiр теориялардың модельдiк компаньондарының қасиеттерi
Свойства модельного компаньона некоторых теорий
Kabidenov A. Kasatova A. Bekenov M.I. Markhabatov N.D.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#114Issue 2114 - 123 pp.
The class K of algebraic systems of signature σ is called a formula-definable class if there exists an algebraic system A of signature σ such that for any algebraic system B of signature σ it is B ∈ K if and only if Th(B) · Th(A) = Th(A). The paper shows that the formula-definable class of algebraic systems is idempotently formula-definable and is an axiomatizable class of algebraic systems. Any variety of algebraic systems is an idempotently formula-definite class. If the class K of all existentially closed algebraic systems of a theory T is formula-definable, then a theory of the class K is a model companion of the theory T. Also, in the paper the examples of some theories on the properties of formula-definability, pseudofiniteness and smoothly approximability of their model companion were discussed.
formula-definable class , model companion , pseudofinite theory , smoothly approximated structure
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L.N. Gumilyov Eurasian National University, 13 Kazhymukan street, Astana, 010008, Kazakhstan
The Medical University of Karaganda, 40 Gogol street, Karaganda, 100000, Kazakhstan
The Algebra and Geometry Department, L.N. Gumilyov Eurasian National University, 13 Kazhymukan street, Astana, 010008, Kazakhstan
L.N. Gumilyov Eurasian National University, Astana, 010000, Kazakhstan
Kazakh-British Technical University, Almaty, Kazakhstan
L.N. Gumilyov Eurasian National University
The Medical University of Karaganda
The Algebra and Geometry Department
L.N. Gumilyov Eurasian National University
Kazakh-British Technical University
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