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

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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/}
}
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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/