Geodesic
Vaught's conjecture for weakly $o$-minimal theories of~finite convexity rank
Izvestiya. Mathematics , Tome 84 (2020) no. 2, pp. 324-347.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that weakly $o$-minimal theories of finite convexity rank having less than $2^{\omega}$ countable models are binary. Our main result is the confirmation of Vaught's conjecture for weakly $o$-minimal theories of finite convexity rank.
Keywords: weak $o$-minimality, Vaught's conjecture, countable model, convexity rank, binarity. 
@article{IM2_2020_84_2_a4,
     author = {B. Sh. Kulpeshov},
     title = {Vaught's conjecture for weakly $o$-minimal theories of~finite convexity rank},
     journal = {Izvestiya. Mathematics },
     pages = {324--347},
     publisher = {mathdoc},
     volume = {84},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_2_a4/}
}
TY  - JOUR
AU  - B. Sh. Kulpeshov
TI  - Vaught's conjecture for weakly $o$-minimal theories of~finite convexity rank
JO  - Izvestiya. Mathematics 
PY  - 2020
SP  - 324
EP  - 347
VL  - 84
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2020_84_2_a4/
LA  - en
ID  - IM2_2020_84_2_a4
ER  - 
%0 Journal Article
%A B. Sh. Kulpeshov
%T Vaught's conjecture for weakly $o$-minimal theories of~finite convexity rank
%J Izvestiya. Mathematics 
%D 2020
%P 324-347
%V 84
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2020_84_2_a4/
%G en
%F IM2_2020_84_2_a4
B. Sh. Kulpeshov. Vaught's conjecture for weakly $o$-minimal theories of~finite convexity rank. Izvestiya. Mathematics , Tome 84 (2020) no. 2, pp. 324-347. http://geodesic.mathdoc.fr/item/IM2_2020_84_2_a4/

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

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

[3] B. Sh. Kulpeshov, “Rang vypuklosti i ortogonalnost v slabo $o$-minimalnykh teoriyakh”, Izv. HAH PK. Ser. fiz.-matem., 2003, no. 1, 26–31 | MR

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

[5] L. L. Mayer, “Vaught's conjecture for o-minimal theories”, J. Symbolic Logic, 53:1 (1988), 146–159 | DOI | MR | Zbl

[6] 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

[7] A. Alibek, B. S. Baizhanov, “Examples of countable models of a weakly o-minimal theory”, Int. J. Math. Phys., 3:2 (2012), 1–8

[8] 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

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

[10] B. S. Baizhanov, B. Sh. Kulpeshov, “On behaviour of $2$-formulas in weakly o-minimal theories”, Mathematical logic in Asia (Novosibirsk, 2005), World Sci. Publ., Hackensack, NJ, 2006, 31–40 | MR | Zbl

[11] A. A. Alibek, B. S. Baizhanov, T. S. Zambarnaya, “Discrete order on a definable set and the number of models”, Matem. zhurn. (Almaty), 14:3(53) (2014), 5–13

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

[13] B. Sh. Kulpeshov, “Criterion for binarity of $\aleph_0$-categorical weakly o-minimal theories”, Ann. Pure Appl. Logic, 145:3 (2007), 354–367 | DOI | MR | Zbl