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    The model theory of the field of reals with a subgroup of the unit circle
    (Wiley, 2008) Belegradek, Oleg; Zilber, Boris
    We describe definable sets in the field of reals augmented by a predicate for a finite rank multiplicative group Gamma of complex numbers contained in the unit circle . This structure interprets the quotient-space /Gamma which, for Gamma infinite cyclic, is related to the quantum torus. Every definable set is proved to be a Boolean combination of existentially definable sets. We give a complete set of axioms for the theory of such a structure.