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SUMMARY:Betweenness reals: How to do Dedekind cuts when you don't know whi
 ch way is up - Peter Johnstone (DPMMS)
DTSTART:20190430T131500Z
DTEND:20190430T141500Z
UID:TALK123664@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:Recently Vaughan Pratt claimed on the categories list that any
  of the standard constructions of the reals from the rationals could be ca
 rried out using only the affine-space structure of the rationals. As I poi
 nted out at the time\, that is not quite true\, because the Dedekind-cuts 
 construction makes essential use of the order-relation on Q\, which is not
  definable from the affine structure since Q has order-reversing affine au
 tomorphisms. However\, Q does have a ternary 'betweenness' relation defina
 ble from its affine structure. In this talk I shall investigate how the De
 dekind-cuts construction can be made to work for spaces equipped with a be
 tweenness structure: the results are mostly predictable\, but there are on
 e or two unexpected twists.
LOCATION:MR4\, Centre for Mathematical Sciences
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