Geodesic
$JSp$-cosemanticness of $R$-modules
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1233-1244.

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The main purpose of this article is to study the model-theoretic properties of $R$-modules within Jonsson theories. We obtain a criterion of $JSp$-cosemanticness of $R$-modules, which generalizes the elementary equivalence of modules. We describe countably categorical perfect existentially closed Jonsson $R$-modules.
Keywords: Jonsson theory, model companion, existentially closed model, perfectness
Mots-clés : cosemanticness, $R$-modules. 
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A. R. Eshkeev; O. I. Ulbrikht. $JSp$-cosemanticness of $R$-modules. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1233-1244. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a20/

[1] K.I. Beidar, A.V. Mikhalev, G.E. Puninski, “Logical aspects of the theory of rings and modules”, Fundamentalnaya i prikladnaya matematika, 1:1 (1995), 1–62 | MR | Zbl

[2] E.I. Bunina, A.V. Mikhalev, “Elementary equivalence of categories of modules over rings, endomorphism rings, and automorphism groups of modules”, Fundamentalnaya i prikladnaya matematika, 10:2 (2004), 51–134 | MR | Zbl

[3] A.R. Yeshkeyev, O.I. Ulbrikht, “JSp-cosemanticness and JSB property of Abelian groups”, Siberian Electronic Mathematical Reports, 13 (2016), 861–874 | MR | Zbl

[4] J. Barwise \(Ed.\), Handbook of mathematical logic, v. 1, Model theory, Nauka, M., 1982 | Zbl

[5] T.G. Mustafin, “Generalized Jonsson Conditions and a Description of Generalized Jonsson Theories of Boolean Algebras”, Siberian Adv. Math., 10:3 (2000), 1–58 | MR | Zbl

[6] A.R. Yeshkeyev, Jonsson theories, KarGU, Karaganda, 2009

[7] W. Hodges, Model Theory, Cambridge University Press, Cambridge, 1993 | MR | Zbl

[8] G.E. Sacks, Saturated Model Theory, Mathematics Lecture Note Series, W. A. Benjamin, Inc. Advanced Book Program, Reading, Mass., 1972 | MR | Zbl

[9] Y.T. Mustafin, “Quelques proprietes des theories de Jonsson”, The Journal of Symbolic Logic, 67:2 (2002), 528–536 | DOI | MR | Zbl

[10] A.R. Yeshkeyev, G.S. Begetayeva, “Stability of $\Delta$-$PM$-theory and its center”, Bulletin of the Karaganda University. Mathematics Series, 4(56) (2009), 29–34

[11] M. Ziegler, “Model theory of modules”, Annals of Pure and Applied Logic, 26 (1984), 149–213 | DOI | MR | Zbl

[12] R. Villemaire, “Theories of modules closed under direct products”, The Journal of Symbolic Logic, 57:2 (1992), 515–521 | DOI | MR | Zbl

[13] B. Poizat, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, Translated by Moses Klein, Springer, New York, NY, 2000 | MR | Zbl

[14] A. Macintyre, “On algebraically closed groups”, Ann. Math., 96 (1972), 53–97 | DOI | MR | Zbl

[15] W. Hodges, A Shorter Model Theory, Cambridge University Press, Cambridge, 1997 | MR | Zbl

[16] W. Baur, “$\aleph_0$-Categorical Modules”, The Journal of Symbolic Logic, 40 (1975), 213–220 | DOI | MR | Zbl