School Seminars and Colloquia

The collection of linear orderings with underlying set w is Borel Complete

School Seminar

by Zachiri McKenzie

Institution: The University of Melbourne
Date: Wed 25th June 2008
Time: 4:15 PM
Location: Room 107, Richard Berry Building, The University of Melbourne

Abstract: In this talk I will present a result due to Harvey Friedman and Lee
Stanley that shows that there exists a Borel mapping from the collection
of all countable infinite graphs into the collection of linear orderings of !
that preserves the isomorphism relationship. Coupled with a well known
result (originally due to Skolem?) this demonstrates that every collection
of countable models of some L!1! sentence can be embedded using a Borel
function into the collection of linear orderings of ! in such a way so as the
isomorphism relation is preserved.

For More Information: Greg Hjorth