English

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.

Keywords

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

R2 v1 2026-06-22T08:57:56.930Z