$JSp$-cosemanticness and JSB property of Abelian groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 861-874.

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The main purpose of this article is to study the model-theoretic properties of Abelian groups within Jonsson theories. The obtained results give us Jonsson analogs for the Schröder–Bernstein property and for the elementary classification of complete theories of Abelian groups.
Keywords: Jonsson theory, model companion, existentially closed model, perfectness
Mots-clés : cosemanticness.
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A. R. Yeshkeyev; O. I. Ulbrikht. $JSp$-cosemanticness and JSB property of Abelian groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 861-874. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a22/

[1] J. Barwise (ed.), Handbook of mathematical logic, v. 1, Model theory, Science, M., 1982 | Zbl

[2] 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

[3] A. R. Yeshkeyev, “On Jonsson stability and some of its generalizations”, Journal of Mathematical Sciences, 166:5 (2010), 646–654 | DOI | MR | Zbl

[4] S. Shelah, Classification theory and the number of non-isomorphic models, Studies in Logic and the Foundations of Mathematics, 1978 | Zbl

[5] A. R. Yeshkeyev, “The structure of lattices of positive existential formulae of ($\Delta$-$PJ$)-theories”, Science Asia. Journal of The Science Society of Thailand, 39:1 (2013), 19–24 | DOI

[6] V. Weispfenning, “The model-theoretic significance of complemented existential formulas”, The Journal of Symbolic Logic, 46:4 (1981), 843–849 | DOI | MR | Zbl

[7] A. R. Yeshkeyev, “Categorical positive Jonsson theories”, Bulletin of the Karaganda University. Mathematics Series, 2006, no. 4(44), 10–16

[8] I. Ben-Yaacov, “Positive model theory and compact abstract theories”, Journal of Mathematical Logic, 3:1 (2003), 85–118 | DOI | MR | Zbl

[9] I. Ben-Yaacov, “Compactness and independence in non first order frameworks”, Bulletin of Symbolic logic, 11:1 (2005), 28–50 | DOI | MR | Zbl

[10] W. Szmielew, “Elementary properties of Abelian groups”, Fundamenta Mathematica, 41 (1955), 203–271 | MR | Zbl

[11] Y. L. Ershov, Problems of solubility and constructive models, Science, M., 1980 | Zbl

[12] L. Fuchs, Infinite Abelian Groups, v. I, Publishing House of Mir, M., 1974 | MR | Zbl

[13] P. C. Eklof, E. R. Fischer, “The elementary theory of abelian groups”, Annals of Math logic, 4 (1972), 115–171 | DOI | MR | Zbl

[14] Y. L. Ershov, E. A. Palyutin, Mathematical logic, Fizmatlit, M., 2011

[15] J. Goodrick, The Schröder–Bernstein property for theories of abelian groups, 2007, arXiv: 0705.1850v1

[16] A. R. Yeshkeyev, Jonsson theories, KarGU, Karaganda, 2009, 250 pp.

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

[18] A. R. Yeshkeyev, “Jonsson classes of Abelian groups”, Buketov meeting, Interuniversity conference dedikaded to the 20th anniversary of the KarSU (Karaganda, 1992), v. 1, 127

[19] A. R. Yeshkeyev, G. S. Begetayeva, “Stability of $\Delta$-$PM$-theory and its center”, Bulletin of the Karaganda University. Mathematics Series, 2009, no. 4(56), 29–34

[20] B. Jonsson, “Homogeneous universal relational systems”, Math. Scand., 8 (1960), 137–142 | DOI | MR | Zbl

[21] J. Goodrick, When are elementarily bi-embeddable models isomorphic?, PhD thesis, University of California, Berkeley, 2007 | MR

[22] T. A. Nurmagambetov, “The mutual embeddability of models”, Theory of Algebraic Structures, Collection of scientific papers, Karaganda, 1985, 109–115 | MR | Zbl

[23] T. A. Nurmagambetov, “Characterization of $\omega$-stable theories with a bounded number of dimensions”, Algebra and Logika, 28:5 (1989), 388–396 | DOI | MR | Zbl

[24] J. Goodrick, M. C. Laskowski, “The Schröder-Bernstein property for $a$-saturated models”, Proc. AMS, 142:3 (2014), 1013–1023 | DOI | MR | Zbl