Vaught's theorem holds for l2 but fails for ln when n > 2

Khaled M. K. M. I., Ahmed T. S.

Bulletin of the Section of Logic, vol.39, no.3-4, pp.107-122, 2010 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 3-4
  • Publication Date: 2010
  • Journal Name: Bulletin of the Section of Logic
  • Journal Indexes: Scopus
  • Page Numbers: pp.107-122
  • Istanbul Medipol University Affiliated: No


Vaught's theorem says that if T is a countable atomic first order theory, then T has an atomic model. Let Ln denote the finite variable fragment of first order logic with n variables. We show that a strong form of Vaught's theorem holds for L2 while it fails for Ln when n > 2. An analogous result is proved for the finite variable fragments without equality.