### Abstract

We show that the Pfaffian closure of an o-minimal structure with analytic cell decomposition is model complete. This is achieved by proving a theorem of the complement for nested sub-Pfaffian sets over the o-minimal structure in question.

## An Isaac Newton Institute Workshop## An Introduction to Recent Applications of Model Theory## The theorem of the complement for nested sub-Pfaffian sets5th April 2005
## AbstractWe show that the Pfaffian closure of an o-minimal structure with analytic cell decomposition is model complete. This is achieved by proving a theorem of the complement for nested sub-Pfaffian sets over the o-minimal structure in question. |