Analytic Zariski structures and non-elementary categoricity

2016/01/12 by Boris Zilber, Zilber, Boris
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1601.02961

openalex publication_date 2016/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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