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VERSION:2.0
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LOCATION:60 Evans
SEQUENCE:0
DTEND:20090501T180000
DTSTART:20090501T161000
UID:philosophy.berkeley.edu:events:537
DTSTAMP:20091124T030443
DESCRIPTION:In 1989 Woodin and others asked whether\, for a singular cardin
 al kappa of cofinality omega\, the tree property at kappa+ implies the sing
 ular cardinal hypothesis (SCH) at kappa.  At the time\, the only models in 
 which SCH failed were obtained by singularizing a regular cardinal where th
 e GCH fails\, and the question was intended to test whether this was the on
 ly way.  Later results by Gitik-Magidor showed that there are other ways\, 
 yet the test question itself persisted.  It has since become a motivator fo
 r several results on square principles\, considered possible intermediaries
  on the way from the tree property to the SCH.\n\nWe settle the question in
  this talk.  We show that the tree property at kappa+ does not imply SCH at
  kappa.  The model where the tree property holds and SCH fails is obtained 
 by forcing with ultrafilters.  We give a survey of this technique and of re
 lated results\, starting with some of the most well known instances.  The t
 alk is self contained and accessible to a general audience in mathematical 
 logic.\n\n
SUMMARY:Logic Colloquium\nItay Neeman\nForcing with Ultrafilters
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