Submission date: 7 June 2022

Abstract:

Given a cover 𝕌 of a family of smooth complex algebraic varieties, we associate with it a class U, containing 𝕌, of structures locally definable in an o-minimal expansion of the reals. We prove that the class is ℵ_0-homogenous over submodels and stable. It follows that U is categorical in cardinality ℵ_1. In the one-dimensional case we prove that a slight modification of U is an abstract elementary class categorical in all uncountable cardinals.

Mathematics Subject Classification: 03C45

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Full text arXiv 2206.03279: pdf, ps.