Model theory is the study of diverse mathematical structures from the perspective of formal logic.
The University of Manchester has long had a strong research group in mathematical logic, dating back at least to the time of Turing. Manchester has hosted the Logic Colloquium, the annual European meeting of the Association for Symbolic Logic, on three occasions, first in 1969, then in 1984 and then again in 2012. Research in logic at Manchester is now focused on model theory and its connections to other parts of mathematics. Model theory studies mathematical structures using logical tools, and has seen major applications to diverse areas of pure mathematics, including number theory and algebra.
We have research interests across a range of topics in model theory, including:
- Model theory of modules
- Connections between model theory, category theory and representation theory
- Stability theoretic methods in groups and fields.
- Model theory of differential fields
- Connections between model theory and group theory, with a special emphasize on groups of finite Morley rank and differential Galois theory
- Model theory of ordered algebraic structures and real algebraic geometry
- Model theory of valued fields
- O-minimal structures, and interactions between model theory and diophantine geometry
- Model theory of classical special functions