# Silver's Theorem

#### by Leigh Humphries

Institution: The University of Melbourne
Date: Wed 13th June 2007
Time: 4:30 PM
Location: Room 107, Richard Berry Building

Abstract: If $E$ is a $\PI_{1}^{1}$ equivalence relation between reals, Silver's
Theorem states that there is a perfect set of pairwise $E$-inequivalent
reals, or there are only countably many $E$-equivalence classes. We
present a proof of the theorem due to Leo Harrington, which is performed
entirely within 2nd order arithmetic.

For More Information: Professor Greg Hjorth Phone: +61 3 8344 0449 G.Hjorth@ms.unimelb.edu.au