On categoricity questions for universal unars and undirected graphs under semantic Jonsson quasivariety
Семантикалық йонсондық квазикөптүрлiлiк аясында универсал унарлар мен бағытталмаған графтар үшiн категориялық мәселелер туралы
О категоричности универсальных унаров и неориентированных графов с позиции семантического йонсоновского квазимногообразия
Yeshkeyev A.R. Yarullina A.R. Amanbekov S.M.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#111Issue 3165 - 180 pp.
The article is devoted to the study of semantic Jonsson quasivarieties of universal unars and undirected graphs. The first section of the article consists of basic necessary concepts from Jonsson model theory. The following two sections are results of using new notions of semantic Jonsson quasivariety of Robinson unars JCU and semantic Jonsson quasivariety of Robinson undirected graphs JCG, its elementary theory and semantic model. In order to prove two main results of the paper, Robinson spectra RSp(JCU) and RSp(JCG) and their partition onto equivalence classes [∆]U and [∆]G by cosemanticness relation were considered. The main results are presented in the form of theorems 11 and 13 and imply following useful corollaries: countably categorical Robinson theories of unars are totally categorical; countably categorical Robinson theories of undirected graphs are totally categorical. The obtained results can be useful for continuation of the various Jonsson algebras’ research, particularly semantic Jonsson quasivariety of S-acts over cyclic monoid.
categoricity , cosemanticness , countable categoricity , graph , Jonsson spectrum , Jonsson theory , quasivariety , Robinson spectrum , Robinson theory , semantic Jonsson quasivariety , unar , undirected graph , universal theory
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Karaganda University of the Name of Academician E.A. Buketov, Institute of Applied Mathematics, Karaganda, Kazakhstan
Karaganda University of the Name of Academician E.A. Buketov
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