Geodesic
On freedom and independence in hypergraphs of models of theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 612-630.

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The notions of freedom and independence for hypergraphs of models of a theory are introduced. We study properties of these notions in general case and for some natural classes of theories. We describe hypergraphs of models for theories of unary predicates, equivalence relations and study the properties of hypergraphs for ordered theories and for theories of unars.
Keywords: hypergraph of models, elementary theory, free set, independent sets, complete union of hypergraphs. 
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B. Sh. Kulpeshov; S. V. Sudoplatov. On freedom and independence  in hypergraphs of models of theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 612-630. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a16/

[1] S. V. Sudoplatov, Classification of countable models of complete theories, NSTU, Novosibirsk, 2018

[2] S. V. Sudoplatov, “On acyclic hypergraphs of minimal prime models”, Siberian Math. J., 42 (2001), 1408–1412 | DOI | MR | Zbl

[3] S. V. Sudoplatov, “Hypergraphs of prime nmodels and distributions of countable models of small theories”, J. of Math. Sciences, 169 (2010), 680–695 | DOI | MR | Zbl

[4] K. A. Baikalova, “On some hypergraphs of prime models and limit models generated by them”, Algebra and Model Theory, 7, Collection of works, eds. A.G. Pinus, K.N. Ponomaryov, S.V. Sudoplatov, NSTU, Novosibirsk, 2009, 6–17 | MR | Zbl

[5] S. V. Sudoplatov, “On the separability of elements and sets in hypergraphs of models of a theory”, Bulletin of Karagandy University. Mathematics series, 82 (2016), 113–120

[6] B. Sh. Kulpeshov, S. V. Sudoplatov, “On hypergraphs of prime models for quite o-minimal theories with small number of countable models”, Annual Scientific April Conference of Institute of Mathematics and Mathematical Modelling devoted to Science Day and Scientific Seminar "Differential operators and modelling complex systems" (DOMCS-2017) devoted to 70-th anniversary of professor M.T. Dzhenaliev, Abstracts of talks (Almaty, 7–8 April 2017), IMMM, Almaty, 2017, 30–32

[7] S. V. Sudoplatov, “Derivative Structures in Model Theory and Group Theory”, International Conference "Actual Problems of Pure and Applied Mathematics" devoted to 100-th anniversary of academician A.D. Taimanov, Abstracts of talks (Almaty, 22–25 August 2017), IMMM, Almaty, 2017, 76–79

[8] B. Sh. Kulpeshov, S. V. Sudoplatov, “On decomposition of hypergraphs of models of a theory. Appendix to theories of unars”, Sintax and Semantics of Logical Systems, Materials of 5-th Russian School-Seminar, Buryatsky State University Publishing House, Ulan-Ude, 2017, 52–56

[9] B. Sh. Kulpeshov, S. V. Sudoplatov, On relative separability in hypergraphs of models of theories, 2018, 11 pp., arXiv: 1802.08088v1 [math.LO]

[10] B. Sh. Kulpeshov, S. V. Sudoplatov, On structures in hypergraphs of models of a theory, 2018, 14 pp., arXiv: 1802.08092v1 [math.LO]

[11] R. Engelking, General Topology, Sigma series in pure mathematics, 6, Revised and completed edition, Heldermann Verlag, Berlin, 1989 | MR | Zbl

[12] B. Sh. Kulpeshov, S. V. Sudoplatov, “Linearly ordered theories which are nearly countably categorical”, Mathematical Notes, 101:3 (2017), 475–483 | DOI | MR | Zbl

[13] H. D. Macpherson, D. Marker, and C. Steinhorn, “Weakly o-minimal structures and real closed fields”, Trans. Amer. Math. Soc., 352:12 (2000), 5435–5483 | DOI | MR | Zbl

[14] B. S. Baizhanov, “Expansion of a model of a weakly o-minimal theory by a family of unary predicates”, The Journal of Symbolic Logic, 66 (2001), 1382–1414 | DOI | MR | Zbl

[15] B. Sh. Kulpeshov, “Convexity rank and orthogonality in weakly o-minimal theories”, News of National Academy of Sciences of the Republic of Kazakhstan, Series physics-mathematics, 227 (2003), 26–31 | MR

[16] B. Sh. Kulpeshov, S. V. Sudoplatov, “Vaught's conjecture for quite o-minimal theories”, Annals of Pure and Applied Logic, 168 (2017), 129–149 | DOI | MR | Zbl

[17] P. Tanović, “Minimal first-order structures”, Annals of Pure and Applied Logic, 162:11 (2011), 948–957 | DOI | MR | Zbl

[18] A. Alibek, B. S. Baizhanov, “Examples of countable models of a weakly o-minimal theory”, International Journal of Mathematics and Physics, 3 (2012), 1–8

[19] B. Sh. Kulpeshov, S. V. Sudoplatov, Distributions of countable models of quite $o$-minimal Ehrenfeucht theories, 2018, 13 pp., arXiv: 1802.08078v1 [math.LO]

[20] S. V. Sudoplatov, Distributions of countable modeld of disjoint unions of Ehrenfeucht theories, 2018, 12 pp., arXiv: 1802.09364v1 [math.LO]

[21] K. Ikeda, A. Pillay, A. Tsuboi, “On theories having three countable models”, Mathematical Logic Quarterly, 44:2 (1998), 161–166 | DOI | MR | Zbl

[22] B. S. Baizhanov, “One-types in weakly o-minimal theories”, Proceedings of Informatics and Control Problems Institute (Almaty, 1996), 75–88

[23] B. S. Baizhanov, B. Sh. Kulpeshov, “On behaviour of $2$-formulas in weakly o-minimal theories”, Mathematical Logic in Asia, Proceedings of the 9th Asian Logic Conference, eds. S. Goncharov, R. Downey, H. Ono, World Scientific, Singapore, 2006, 31–40 | DOI | MR | Zbl

[24] B. Sh. Kulpeshov, “Weakly o-minimal structures and some of their properties”, The Journal of Symbolic Logic, 63:4 (1998), 1511–1528 | DOI | MR | Zbl