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SUMMARY:Free groups and the Axiom of Choice - Kleppmann\, P (University of
  Cambridge)
DTSTART:20151010T130000Z
DTEND:20151010T135500Z
UID:TALK61443@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:The role of the Axiom of Choice in Mathematics has been studie
 d extensively. Given a theorem of ZFC\, one may ask how strong it is compa
 red to the Axiom of Choice. Although a large collection of results has bee
 n 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.\n\nI will introduce recent 
 results that help to establish the strength of Nielsen-Schreier\, focussin
 g on the method of representative functions. \nThen I discuss potential ap
 plications of this technique to other algebraic structures admitting a bas
 is\, such as free abelian groups and vector spaces.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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