On a theorem of Vaught for first order logic with finitely many variables

Journal of Applied Non-Classical Logics 19 (1):97-112 (2009)
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Abstract

We prove that the existence of atomic models for countable atomic theories does not hold for Ln the first order logic restricted to n variables for finite n > 2. Our proof is algebraic, via polyadic algebras. We note that Lnhas been studied in recent times as a multi-modal logic with applications in computer science. 2000 MATHEMATICS SUBJECT CLASSIFICATION. 03C07, 03G15.

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10.3166/jancl.19.97-112

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Cylindric Algebras. Part I.Leon Henkin, J. Donald Monk, Alfred Tarski, L. Henkin, J. D. Monk & A. Tarski - 1985 - Journal of Symbolic Logic 50 (1):234-237.
Cylindric algebras.Leon Henkin - 1971 - Amsterdam,: North-Holland Pub. Co.. Edited by J. Donald Monk & Alfred Tarski.
On the existence of atomic models.M. C. Laskowski & S. Shelah - 1993 - Journal of Symbolic Logic 58 (4):1189-1194.
Algebraic Logic, Where Does It Stand Today?Tarek Sayed Ahmed - 2005 - Bulletin of Symbolic Logic 11 (3):465-516.

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