Analytic Zariski structures and non-elementary categoricity
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Publication:5221585
zbMATH Open1433.03091arXiv1601.02961MaRDI QIDQ5221585
Publication date: 2 April 2020
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.
Full work available at URL: https://arxiv.org/abs/1601.02961
Classification theory, stability, and related concepts in model theory (03C45) Models of other mathematical theories (03C65) Categoricity and completeness of theories (03C35) Abstract elementary classes and related topics (03C48) Foundations of algebraic geometry (14A99)
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