BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The tree property (session 1) - Sinapova\, D (Univ
ersity of Illinois at Chicago)
DTSTART;TZID=Europe/London:20150824T113000
DTEND;TZID=Europe/London:20150824T123000
UID:TALK60435AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60435
DESCRIPTION:The tree propperty at $kappa$ says that every tree
of height $kappa$ and levels of size less than $k
appa$ has a cofinal branch. A long term project in
set theory is to get the consistency of the tree
property at every regular cardinal greater than $
leph_1$. So far we only know that it is possible t
o have the tree property up to $leph_{omega+1}$\,
due to Neeman. The next big hurdle is to obtain i
t both at $leph_{omega+1}$ and $leph_{omega+2}$
when $leph_omega$ is trong limit. Doing so would
require violating the singular cardinal hypothesis
at $leph_omega$. \n\nIn this tutorial we will st
art with some classic facts about the tree propert
y\, focusing on branch lemmas\, successors of sing
ulars and Prikry type forcing used to negate SCH.
We will then go over recent developments including
a dichotomy theorem about which forcing posets ar
e good candidates for getting the tree property at
$leph_{omega+1}$ together with not SCH at $leph
_omega$. Finally\, we will discuss the problem of
obtaining the tree property at the first and doubl
e successors of a singular cardinal simultaneously
.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
END:VEVENT
END:VCALENDAR