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.