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.