### Models, sets and classifications

Project Type: Prin 2022

Funded by: MUR

Period: Sep 28, 2023 – Sep 27, 2025

Budget: €35.027,00

Principal Investigator: Gianluca Paolini (Università di Torino)

Local coordinator: Alessandro Berarducci (Università di Pisa)

##### Participants

Marcello Mamino (Università di Pisa)

##### Description

Mathematical logic is an ever-growing field within mathematics. Originally motivated by foundational and philosophical questions, its methods have now evolved into very fine tools which have found profound applications in many branches of mathematics. Among the main subfields of mathematical logic, the project focuses on axiomatic set theory, computability theory, descriptive set theory and model theory. Motivated by both internal and external questions, all these fields have developed over the years into advanced technologies which interact with each other and which have found striking applications in mainstream mathematics. Our long-established research network specializes in these four sectors of mathematical logic, with emphasis on classification questions and concrete applications to mathematics.
The scientific goals of our project have a broad range. We plan to achieve progress towards:
- the question of decidability of the real exponential field;
- Zilber’s conjecture on the complex exponential field;
- connections between surreal numbers and transseries;
- generalizations of Herzog’s work on universal enveloping algebras;
- model theory of Steiner systems and connections with relevant combinatorics;
- classification problems in group theory from the perspective of descriptive set theory;
- model theory of groups and of ordered abelian groups;
- automorphism groups of ultrametric Polish spaces;
- generalized descriptive set theory for singular cardinals;
- connections between reverse mathematics and Weihrauch reducibility.