BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Saturated Boolean Ultrapowers - Parente\, F (University of East An
 glia)
DTSTART:20151009T134000Z
DTEND:20151009T143500Z
UID:TALK61416@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:In this talk I will survey the general theory of Boolean ultra
 powers\, starting from the beginnings and including many applications and 
 some possible future developments. Also\, the set-theoretic approach to Bo
 olean ultrapowers\, due to recent work of Hamkins and Seabold\, will be di
 scussed.\n\nFirst developed by Mansfield as a purely algebraic constructio
 n\, Boolean ultrapowers are a natural generalization of usual power-set ul
 trapowers. More specifically\, I will focus on how some combinatorial prop
 erties of a ultrafilter U are related to the realization of types in the r
 esulting Boolean ultrapower. Many results on $lambda$-regular and $lambda$
 -good \nultrafilters\, mostly due to Keisler\, can be generalized to this 
 context. In particular\, I will sketch the construction of a $lambda$-good
  ultrafilter on the Levy collapsing algebra $mathrm{Coll}(lambda\, <lambda
 )$. In addition to that\, I will describe a possible application to Keisle
 r's order on complete theories.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
END:VEVENT
END:VCALENDAR