On Jonsson varieties and quasivarieties
Йонсондық көптүрлiлiк және квазикөптүрлiлiк туралы
О йонсоновских многообразиях и квазимногообразиях
Yeshkeyev A.R.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#104Issue 4151 - 157 pp.
In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory, J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closedness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question.
Jonsson quasivariety , Jonsson spectrum , Jonsson theory , Jonsson variety , semantic model
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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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