Series: Penn State Logic Seminar

Date: Tuesday, September 7, 2004

Time: 2:30 - 3:45 PM

Place: 307 Boucke Building

Speaker: John Clemens, Penn State, Mathematics

Title: Structures With Many Automorphisms

Abstract: 

  Descriptive set theory can be used to gauge the complexity of
  classifying various collections of countable structures up to
  isomorphism.  We generally expect symmetric structures (ones with
  large automorphism groups) to be easier to classify. In several
  situations, though, this turns out not to be the case.  One example
  is the theory of graphs, where classifying vertex-transitive graphs
  up to isomorphism turns out to be just as complicated (in a sense I
  will make precise) as classifying all graphs up to isomorphism.  I
  will discuss the general theory of classifying countable structures
  and explain how a result of Mekler allows us to find complexity even
  among certain symmetric structures.