Vaughts theorem holds for L2 but fails for Ln when n> 2
Mohamed Khaled, Tarek Sayed Ahmed · 2010
Vaught’s theorem says that if T is a countable atomic rst order theory, then T has an atomic model. Let Ln denote the nite variable fragment of rst 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 nite variable fragments without equality. Let L be a