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arXiv · 1601.02961

Analytic Zariski structures and non-elementary categoricity

Boris Zilber
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Abstract

We study analytic Zariski structures from the point of view of non-elementary model theory. We show how to associate an abstract elementary class with a one-dimensional analytic Zariski structure and prove that the class is stable, quasi-minimal and homogeneous over models. We also demonstrate how Hrushovski's predimension arises in this general context as a natural geometric notion and use it as one of our main tools.

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Boris Zilber. 2016-01-12. Analytic Zariski structures and non-elementary categoricity. https://arxiv.org/abs/1601.02961

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