Title: Whitehead's Problem And Reverse Mathematics
 
Speaker: Prof. YANG Yue（Department of Mathematics, National University of
Singapore）
 
Time: December 12, Friday, 4:00~5:00pm
 
Location: New Main Building, Room 1220, Beijing Normal University
 
Abstract:
 
Whitehead's problem asks if every W-group is free. In 1951, Stein proved that every countable W-group is free. In mid 1970s, Shelah proved that Whitehead’s problem is independent of ZFC, a surprising result as Whitehead’s Problem seems purely algebraic and to have nothing to do with set theory. I will talk about a recent result on Whitehead's Problem in the context of reverse mathematics. This is a joint work with F.Stephan, S.Yang and L.Yu. We established that over the base theory WKL_0, Stein’s Theorem is equivalent to ACA_0.
 
There are two objectives of my talk: One is to introduce the area of reverse mathematics to a more general audience; the other is to explain some new insight about the notion of W-groups. The terminology such as WKL_0, ACA_0 and W-group will be introduced in the talk.