Kutztown University Department of Mathematics

Colloquium

3:30 p.m.

January 29, 2008

Academic Forum 103

Reducts of Countably Categorical Graphs

Dr. Amy Yun Lu

Kutztown University of Pennsylvania

Abstract

Model theory is the branch of logic studying mathematical structures by considering first-order sentences which are true of those structures and the sets which are definable in those structures by first-order formulas. Model theory, algebra and graph theory are often closely related.

Let M be a countably categorical structure, homogeneous for a finite relational language. A reduct of M corresponds, up to bi-interpretability, to a closed subgroup of Sym(M) containing Aut(M). In this talk, I will describe classifications of reducts given by Higman, Thomas and Bennett. I will also present my own results classifying reducts of the random bipartite graph and the random bipartite graph having more than two cross types.

3:00 p.m. refreshments served

3:30 p.m. talk begins

Kutztown Univ. of Pennsylvania Dept. of Mathematics Dr. Paul Ache, Chair