Resumen de The model theory of the field of reals with a subgroup of the unit circle

Oleg Belegradek, Boris Zilber

• We describe definable sets in the field of reals augmented by a predicate for a finite rank multiplicative group of complex numbers contained in the unit circle . This structure interprets the quotient-space / which, for 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