Download this article
Download this article For screen
For printing
Recent Issues
Volume 4, Issue 1
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
 
ISSN 2832-904X (online)
ISSN 2832-9058 (print)
 
Author index
To appear
 
Other MSP journals
Zilber's notion of logically perfect structure: universal covers

John T. Baldwin and Andrés Villaveces
Vol. 3 (2024), No. 2, 647–683
DOI: 10.2140/mt.2024.3.647
Abstract

We sketch the mathematical background and the main ideas in the proofs of categoricity of theories of several examples of universal covers — reducing an analytic to a model theoretic (discrete) description. We hope this discussion will be useful to a wide spectrum of mathematicians, ranging from those working in geometry to those working in logic; specifically, model theory.

Keywords
model theory, infinitary logic, model theory of covers, abelian varieties, Shimura varieties, modular invariants, categoricity
Mathematical Subject Classification
Primary: 03C45, 03C75, 03C98, 11U09, 12L12
Secondary: 03-03
Milestones
Received: 8 February 2023
Revised: 7 September 2023
Accepted: 26 September 2023
Published: 19 July 2024
Authors
John T. Baldwin
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Chicago, IL
United States
Andrés Villaveces
Departamento de Matemáticas
Universidad Nacional de Colombia
Bogotá
Colombia
© 2024 MSP (Mathematical Sciences Publishers).