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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Saturated Boolean Ultrapowers - Parente\, F (Unive
rsity of East Anglia)
DTSTART;TZID=Europe/London:20151009T144000
DTEND;TZID=Europe/London:20151009T153500
UID:TALK61416AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61416
DESCRIPTION:In this talk I will survey the general theory of B
oolean ultrapowers\, starting from the beginnings
and including many applications and some possible
future developments. Also\, the set-theoretic appr
oach to Boolean ultrapowers\, due to recent work o
f Hamkins and Seabold\, will be discussed.\n\nFirs
t developed by Mansfield as a purely algebraic con
struction\, Boolean ultrapowers are a natural gene
ralization of usual power-set ultrapowers. More sp
ecifically\, I will focus on how some combinatoria
l properties of a ultrafilter U are related to the
realization of types in the resulting Boolean ult
rapower. Many results on $lambda$-regular and $lam
bda$-good \nultrafilters\, mostly due to Keisler\,
can be generalized to this context. In particular
\, I will sketch the construction of a $lambda$-go
od ultrafilter on the Levy collapsing algebra $mat
hrm{Coll}(lambda\,