On Quasiminimal Excellent Classes

TL;DR

This paper provides a detailed exposition of Zilber's quasiminimal excellent classes, demonstrating their categoricity and introducing two new results that simplify their definability assumptions and show they are determined by their countable models.

Contribution

It shows that the L_{w1,w}(Q)-definability assumption can be omitted and that each class is uniquely determined by its countable model, advancing the understanding of these classes.

Findings

Dropping the L_{w1,w}(Q)-definability assumption.

Each class is determined by its model of dimension aleph_0.

Enhanced understanding of categoricity in quasiminimal classes.

Abstract

A careful exposition of Zilber's quasiminimal excellent classes and their categoricity is given, leading to two new results: the L_w1,w(Q)-definability assumption may be dropped, and each class is determined by its model of dimension aleph_0.