### Graduate Student Seminar, 4:45pm November 24, 2003

#### Speaker:

Sara Miller
#### Title:

Comparing classes of finite structures
#### Abstract:

In many branches of mathematics, there is work classifying a collection of objects, up to isomorphism or other
important equivalence, in terms of nice invariants. In this talk I will be discussing work done this past summer by
Julia Knight, Wesley Calvert, Desmond Cummins, and myself. Our goal was to compare classes of structures using a
notion of *computable embedding*. If one class of structures can be computably embedded in another, then
structures in the original class are isomorphic only when their embedded copies are isomorphic in the new class. What
resulted from these embeddings is a partial order on classes of structures. We have some "landmark" classes -- finite
prime fields, finite linear orderings, finite dimensional vector spaces over the rationals, and arbitrary linear
orderings -- forming a strictly increasing sequence, with incomparable classes in between.

To volunteer to give a talk, or for any other questions regarding this schedule, contact Wesley Calvert