Abstract:
A common technique in model theory is to classify the definable sets for a
given structure. o-minimal structures, in which all definable subsets of a
model are finite unions of intervals, form the simplest class of ordered
structures, and turn out to have two nice properties:
- all elementarily equivalent models are also o-minimal (every
o-minimal structure has an o-minimal theory), and
-
in an o-minimal structure M, the definable subsets of M^n are as
simple as possible (cell-decomposition).
In recent years, model theorists have pioneered the study the class of
weakly o-minimal structures, in which all definable subsets are finite
unions of convex sets. Unfortunately both (1) and (2) above fail in
general in the weakly o-minimal situation. We examine special cases to get
an idea of the relationship between the two properties, and what
restrictions we may add to a weakly o-minimal structure to ensure that one
or both are satisfied.
Time: 3:45, Thursday Jan 25, 2007
Reception at 3:30.