On a theorem of Vaught for first order logic with finitely many variables - Ahmed, Tarek Sayed (Journal of applied non-classical logics, 2009)
We prove that the existence of atomic models for countable atomic theories does not hold for L n the first order logic restricted to n variables for finite n > 2. Our proof is algebraic, via polyadic algebras. We note that L n has been studied in recent times as a multi-modal logic with applications in computer science. 2000 MATHEMATICS SUBJECT CLASSIFICATION. 03C07, 03G15.