On almost omega-categoricity of weakly o-minimal theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 247-254.

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Here we prove that weakly o-minimal theories of finite convexity rank having less than $2^{\omega}$ countable models are almost $\omega$-categorical.
Keywords: almost $\omega$-categoricity, weak o-minimality, convexity rank, binary theory.
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A. B. Altayeva; B. Sh. Kulpeshov. On almost omega-categoricity of weakly o-minimal theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 247-254. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a3/

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

[2] M. Dickmann, “Elimination of quantifiers for ordered valuation rings”, J. Symb. Log., 52 (1987), 116–128 | DOI | MR | Zbl

[3] B.S. Baizhanov, “Expansion of a model of a weakly o-minimal theory by a family of unary predicates”, J. Symb. Log., 66:3 (2001), 1382–1414 | DOI | MR | Zbl

[4] 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

[5] B. Sh. Kulpeshov, “Countably categorical quite o-minimal theories”, J. Math. Sci., 188:4 (2013), 387–397 | DOI | MR | Zbl

[6] D. Yu. Emel'yanov, B. Sh. Kulpeshov, S.V. Sudoplatov, “Algebras of distributions of binary isolating formulas for quite o-minimal theories”, Algebra Logic, 57:6 (2019), 429–444 | DOI | MR | Zbl

[7] B. Sh. Kulpeshov, “Weakly o-minimal structures and some of their properties”, J. Symb. Log., 63:4 (1998), 1511–1528 | DOI | MR | Zbl

[8] K. Ikeda, A. Pillay, A. Tsuboi, “On theories having three countable models”, Math. Log. Q, 44:2 (1998), 161–166 | DOI | MR | Zbl

[9] S.V. Sudoplatov, Classification of countable models of complete theories, v. 1, Novosibirsk State Technical University Publishing House, Novosibirsk, 2018

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

[11] A.B. Altayeva, B. Sh. Kulpeshov, “Binarity of almost $\omega$-categorical quite o-minimal theories”, Sib. Math. J., 61:3 (2020), 379–390 | DOI | MR | Zbl

[12] B. Sh. Kulpeshov, T.S. Mustafin, “Almost $\omega$-categorical weakly o-minimal theories of convexity rank 1”, Sib. Math. J., 62:1 (2021), 52–65 | DOI | MR | Zbl

[13] R.E. Woodrow, Theories with a finite number of countable models and a small language, Ph.D. Thesis, Simon Fraser University, 1976 | MR

[14] B. Herwig, H.D. Macpherson, G. Martin, A. Nurtazin, J.K. Truss, “On $\aleph_0$-categorical weakly o-minimal structures”, Ann. Pure Appl. Logic, 101:1 (2000), 65–93 | DOI | MR | Zbl

[15] B. Sh. Kulpeshov, S.V. Sudoplatov, “Vaught's conjecture for quite o-minimal theories”, Ann. Pure Appl. Logic, 168:1 (2017), 129–149 | DOI | MR | Zbl

[16] A. Alibek, B.S. Baizhanov, B. Sh. Kulpeshov, T.S. Zambarnaya, “Vaught's conjecture for weakly o-minimal theories of convexity rank 1”, Ann. Pure Appl. Logic, 169:11 (2018), 1190–1209 | DOI | MR | Zbl

[17] B. Sh. Kulpeshov, “Vaught's conjecture for weakly o-minimal theories of finite convexity rank”, Izv. Math., 84:2 (2020), 324–347 | DOI | MR | Zbl

[18] B. Sh. Kulpeshov, “Maximality of the countable spectrum in small quite o-minimal theories”, Algebra Logic, 58:2 (2019), 137–143 | DOI | MR | Zbl

[19] B. Sh. Kulpeshov, “Criterion for binarity of $\aleph_0$-categorical weakly o-minimal theories”, Ann. Pure Appl. Logic, 45:3 (2007), 354–367 | DOI | MR | Zbl