Fri Aug 28, 2015–Sat Aug 29, 2015
60 Evans Hall, 11:10 PM–1 AM
Antonio Montalban (Associate Professor of Mathematics, UC Berkeley)
Analytic Equivalence Relations with ℵ_1-many Classes
We will survey the new results connecting Vaught’s conjecture and computability theory. We will look at some of these result from the more general viewpoint of analytic equivalence relations.
There are two types of results we will concentrate on. On the one hand are the ones about equivalence relations satisfying hyperarithmetic-is-recursive, which provide a purely computability theoretic equivalent to Vaught’s conjecture. On the other hand are the ones about equivalence relations on the natural numbers that are “intermediate,” which I hope will eventually provide another equivalent statement.