## Categoricity.

**Bradd Hart**(Fields Institute)

Having a simple description of a mathematical structure which determines
it

up to isomorphism is desirable in many parts of mathematics. If the

description is intended to be in first order logic and the structure is

infinite, this is not possible. There are some structures where their
first

order theory together with their cardinality determines their isomorphism

type - these structures are called categorical. I will give a survey
of the

subject of categorical first order theories and give some indications of
its

connections with combinatorial geometry, algebraic geometry and permutation

groups. No previous knowledge of logic or model theory will be assumed.