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Department of Mathematics


Logic studies formal languages and reasoning, often focusing on the interplay between axiomatic theories and their models.

Academic staff

Research Fellows

  • Raymond McCulloch

The University of Manchester has a long and distinguished tradition for research in logic, dating back at least to the time of Alan Turing. The University of Manchester has hosted the Logic Colloquium, the European summer meeting of the Association for Symbolic Logic in 1969, 1984 and 2012.

Research in logic at Manchester is now focused on model theory, categorical logic and their connections to other parts of mathematics.

Model theory studies mathematical structures using logical tools, and has seen several major applications to diverse areas of pure mathematics, including number theory and algebra.

Categorical logic studies logic using techniques of category theory, which have led to many surprising applications to algebra, topology and computer science.

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 emphasis 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
  • Type theory, especially homotopy type theory and univalent foundations, and computer-assisted proof-checking
  • Applications of higher-dimensional category theory to logic