TY - JOUR

T1 - Vaught's conjecture for quite o-minimal theories

AU - Kulpeshov, B. Sh

AU - Sudoplatov, S. V.

N1 - Publisher Copyright: © 2016 Elsevier B.V.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We study Vaught's problem for quite o-minimal theories. Quite o-minimal theories form a subclass of the class of weakly o-minimal theories preserving a series of properties of o-minimal theories. We investigate quite o-minimal theories having fewer than 2ω countable models and prove that the Exchange Principle for algebraic closure holds in any model of such a theory and also we prove binarity of these theories. The main result of the paper is that any quite o-minimal theory has either 2ω countable models or 6a3b countable models, where a and b are natural numbers.

AB - We study Vaught's problem for quite o-minimal theories. Quite o-minimal theories form a subclass of the class of weakly o-minimal theories preserving a series of properties of o-minimal theories. We investigate quite o-minimal theories having fewer than 2ω countable models and prove that the Exchange Principle for algebraic closure holds in any model of such a theory and also we prove binarity of these theories. The main result of the paper is that any quite o-minimal theory has either 2ω countable models or 6a3b countable models, where a and b are natural numbers.

KW - Binary theory

KW - Countable model

KW - Quite o-minimal theory

KW - Vaught's conjecture

KW - Weak o-minimality

UR - http://www.scopus.com/inward/record.url?scp=84994784113&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2016.09.002

DO - 10.1016/j.apal.2016.09.002

M3 - Article

AN - SCOPUS:84994784113

VL - 168

SP - 129

EP - 149

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 1

ER -