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arXiv · 1503.06045

Notes on a model theory of quantum 2-torus for generic q

Masanori Itai·Boris Zilber
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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.

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Masanori Itai, Boris Zilber. 2015-03-20. Notes on a model theory of quantum 2-torus for generic q. https://arxiv.org/abs/1503.06045

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