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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Free groups and the Axiom of Choice - Kleppmann\,
P (University of Cambridge)
DTSTART;TZID=Europe/London:20151010T140000
DTEND;TZID=Europe/London:20151010T145500
UID:TALK61443AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61443
DESCRIPTION: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 Axi
om of Choice. Although a large collection of resul
ts 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 f
ree.\n\nI will introduce recent results that help
to establish the strength of Nielsen-Schreier\, fo
cussing on the method of representative functions.
\nThen I discuss potential applications of this t
echnique to other algebraic structures admitting a
basis\, such as free abelian groups and vector sp
aces.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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