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Saturday 10 October 2015, 14:00-14:55
Free groups and the Axiom of Choice
- đ¤ Speaker: Kleppmann, P (University of Cambridge)
- đ Date & Time: Saturday 10 October 2015, 14:00 - 14:55
- đ Venue: Seminar Room 1, Newton Institute
Abstract
The role of the Axiom of Choice in Mathematics has been studied extensively. Given a theorem of ZFC , one may ask how strong it is compared to the Axiom of Choice. Although a large collection of results has been analysed in this way, there are still simple and elegant theorems that offer resistance. One such result is the Nielsen-Schreier theorem, which states that subgroups of free groups are free.
I will introduce recent results that help to establish the strength of Nielsen-Schreier, focussing on the method of representative functions. Then I discuss potential applications of this technique to other algebraic structures admitting a basis, such as free abelian groups and vector spaces.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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