In this paper, we study the field of algebraic numbers with a set of elements of small height treated as a predicate. We prove that such structures are not simple and have the independence property. A real algebraic integer >1 is called a Salem number if and 1/ are Galois conjugate and all other Galois conjugates of lie on the unit circle. It is not known whether 1 is a limit point of Salem numbers. We relate the simplicity of a certain pair with Lehmer's conjecture and obtain a model-theoretic characterization of Lehmer's conjecture for Salem numbers.