B. Sh. Kulpeshov, “Vaught's conjecture for weakly <nobr>$o$</nobr>-minimal theories of finite convexity rank”, Izv. RAN. Ser. Mat., 2020, Volume 84, Issue 2,Pages <nobr>126

This article is cited in 12 papers

Vaught's conjecture for weakly $o$-minimal theories of finite convexity rank

B. Sh. Kulpeshov^abc

^a Kazakh-British Technical University
^b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan
^c Novosibirsk State Technical University

Abstract: 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.

UDC: 510.67

MSC: Primary 03C64; Secondary 03C15, 03C07, 03C50

Received: 13.01.2019

DOI: 10.4213/im8894