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SUMMARY:Ultrafilters\, ultraproducts and ultracategories - Richard Garner\
 , Macquarie University\, Sydney\, Australia
DTSTART:20170810T131500Z
DTEND:20170810T141500Z
UID:TALK75761@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:Consider the following notions: ultrafilter\; ultrapower\; pro
 duct of\nultrafilters\; ultraproduct\; dependent sum of ultrafilters\; the
  category\nof ultrafilters. Building on an old observation of Reinhard B\\
 "orger\, we\nexplain how each of these is forced upon you as soon as you k
 now what it\nmeans for a functor to preserve finite coproducts.\n\nIf time
  permits\, we go on to describe a bicategory W arising naturally\nfrom the
 se considerations\, and explain how the category of models and\nelementary
  embeddings for any classical first-order theory (i.e.\,\nBoolean pretopos
 ) can be seen as a W-enriched category. This seems to be\nrelated to Makka
 i's "Stone duality for first-order logic".
LOCATION:MR5\, Centre for Mathematical Sciences
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