## Eric Rosen

## Technion

## Preservation Theorems and Finite Model Theory

- DIMACS Center - Room 431
- Busch Campus
- Piscataway, New Jersey
- February 9, 2:30 P.M.

### Abstract:

One area of interest in finite model theory has been the attempt
to determine which theorems from classical model theory remain
true over the class of finite structures.
It is well known that many results from classical model theory
no longer hold when relativized to the finite case. For example,
Tait showed that the Existential preservation theorem--every
first order sentence that defines a class of models that
is closed under extensions is equivalent to an existential
sentence--does not hold over the class of finite structures.
In this talk, I will provide some general background in this area,
and discuss some work that grew out of an attempt to
find 'generalized preservation theorems' that hold over finite
structures.