Vaught's conjecture for quite o-minimal theories

B. Sh Kulpeshov, S. V. Sudoplatov

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)129-149
Number of pages21
JournalAnnals of Pure and Applied Logic
Volume168
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Binary theory
  • Countable model
  • Quite o-minimal theory
  • Vaught's conjecture
  • Weak o-minimality

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