%0 Journal Article
%T Notes on a model theory of quantum 2-torus for generic q
%A Masanori Itai
%A Boris Zilber
%J Mathematics
%D 2015
%I arXiv
%X We describe a structure over the complex numbers associated with the non-commutative algebra Aq called quantum 2-tori. These turn out to have uncountably categorical L_omega1,omega-theory, and are similar to other pseudo-analytic structures considered by the second author. The first-order theory of a quantum torus for generic q interprets arithmetic and so is unstable and undecidable. But certain interesting reduct of the structure, a quantum line bundle, is superstable.
%U http://arxiv.org/abs/1503.06045v1