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

Author: 

Belegradek, O
Zilber, B

Publication Date: 

1 January 2008

Journal: 

Journal of the London Mathematical Society

Last Updated: 

2021-10-19T13:17:51.687+01:00

Issue: 

3

Volume: 

78

DOI: 

10.1112/jlms/jdn037

page: 

563-579

abstract: 

We describe definable sets in the field of reals augmented by a predicate for a finite rank multiplicative group Γ of complex numbers contained in the unit circle . This structure interprets the quotient-space /Γ which, for Γ 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. © 2008 London Mathematical Society.

Symplectic id: 

4479

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article