Notes on a model theory of quantum 2-torus for generic q
Logic
2015-03-23 v1
Abstract
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.
Cite
@article{arxiv.1503.06045,
title = {Notes on a model theory of quantum 2-torus for generic q},
author = {Masanori Itai and Boris Zilber},
journal= {arXiv preprint arXiv:1503.06045},
year = {2015}
}
Comments
17 pages