Belegradek, OlegZilber, Boris2024-07-182024-07-1820080024-61071469-7750https://doi.org/10.1112/jlms/jdn037https://hdl.handle.net/11411/7863We 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.eninfo:eu-repo/semantics/closedAccessThe model theory of the field of reals with a subgroup of the unit circleArticle2-s2.0-5644909954610.1112/jlms/jdn037579Q156378Q2WOS:000260976000002