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DTSTART:19700329T010000
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CATEGORIES:Category Theory Seminar
SUMMARY:Betweenness reals: How to do Dedekind cuts when yo
u don't know which way is up - Peter Johnstone (DP
MMS)
DTSTART;TZID=Europe/London:20190430T141500
DTEND;TZID=Europe/London:20190430T151500
UID:TALK123664AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/123664
DESCRIPTION:Recently Vaughan Pratt claimed on the categories l
ist that any of the standard constructions of the
reals from the rationals could be carried out usin
g only the affine-space structure of the rationals
. As I pointed out at the time\, that is not quite
true\, because the Dedekind-cuts construction mak
es essential use of the order-relation on Q\, whic
h is not definable from the affine structure since
Q has order-reversing affine automorphisms. Howev
er\, Q does have a ternary 'betweenness' relation
definable from its affine structure. In this talk
I shall investigate how the Dedekind-cuts construc
tion can be made to work for spaces equipped with
a betweenness structure: the results are mostly pr
edictable\, but there are one or two unexpected tw
ists.
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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