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Model theory is an active branch of mathematical logic. It has many applications to other areas of pure and applied mathematics. Model theory studies the relationship between mathematical structures and the language we use to describe them.

There are two main foci to research in model theory. Pure model theory aims to classify all mathematical structures, creating a ‘geography of mathematics.’ This attempts to show that whole groups of seemingly different mathematical objects share certain fundamental properties. For example, in the tamest structures one obtains a canonical notion of dimension; which enables the development of a geometry in this context. The current drive is to extend this type of result to less tame structures.

Applied model theory looks at the application of this classification to specific structures, giving new insights in many areas of mathematics. The study of o-minimal structures led to new developments in real geometry and analytic number theory; that of differentially closed fields gives an algebraic and geometric description of the solution sets of differential equations. These are currently very active areas and have attracted non-logicians to model theory.

The UCLan model theory group is working on both pure and applied model theory. More specifically we are interested in:

- Links between category theory and model theory
- Measurable and generalised measurable structures.
- Model theory of differential equations.
- Model theory of fields and valued fields.
- O-minimality
- Pseudofinite structures
- Topological dynamics

Model theory is a thriving subject in the UK. The UCLAN group holds a weekly seminar, we also hold the grant for the LMS research group, LYMOTS, which runs a regular joint meeting with Manchester and Leeds.