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SUMMARY:Jessica Schirle (University of California Irvine)
DTSTART:20240307T190000Z
DTEND:20240307T200000Z
DTSTAMP:20260423T035744Z
UID:OLS/150
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/150/">Ga
 ming Models by Buildings</a>\nby Jessica Schirle (University of California
  Irvine) as part of Online logic seminar\n\n\nAbstract\nIn continuous mode
 l theory\, as in the classical setting\, if one has an appropriately sized
  unstable structure A in a countable language\, then depending on the trut
 h of CH\, there's either a unique or 2<sup>c</sup> many nonisomorphic ultr
 apowers of A as we vary the choice of ultrafilter on ω. A similar stateme
 nt may be made in regards to ultraproducts and sequences of structures tha
 t exhibit an order property.\n\nIn a partial answer to a question of Gromo
 v\, Kramer et al. showed that there is a finitely presented group such tha
 t\, depending on the truth of CH\, this group has either a unique or 2<sup
 >c</sup> many asymptotic cones up to homeomorphism. Asymptotic cones of me
 tric spaces are realized as particular metric ultraproducts. The Kramer et
  al. paper does not formalize the obvious model theoretic connection\, but
  does comment on the combinatorial-geometric structure of the asymptotic c
 ones\, which was known to Thornton (and independently to Kramer and Tent) 
 and is a certain kind of building.\n\nIn this talk\, we'll give a brief ov
 erview of work done by Luther to formalize this model theoretic connection
 . Special attention will be given to Ehrenfeucht-Fraïssé games and how t
 he building structure can give us additional tools to develop a possible w
 inning strategy for Player II in games between (what are potentially) non-
 homeomorphic asymptotic cones of certain symmetric spaces.\n
LOCATION:https://researchseminars.org/talk/OLS/150/
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