Non-elementary categoricity and projective locally o-minimal classes

Abstract

Given a cover $\mathbb{U}$ of a family of smooth complex algebraic varieties, we associate with it a class $\mathcal{U},$ containing $\mathbb{U}$, of structures locally definable in an o-minimal expansion of the reals. We prove that the class is ${\aleph }_0$-homogenous over submodels and stable. It follows that $\mathcal{U}$ is categorical in cardinality ${\aleph }_1.$ In the one-dimensional case we prove that a slight modification of $\mathcal{U}$ is an abstract elementary class categorical in all uncountable cardinals.

Cited by in corpus (1)

• Zilber's notion of logically perfect structure: Universal Covers