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SUMMARY:Prikry type sequences: a composition of interconnected results - F
 uchs\, G (City University of New York)
DTSTART:20150827T140000Z
DTEND:20150827T150000Z
UID:TALK60479@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:I would like to survey a series of beautiful and almost myster
 ious properties of Prikry sequences which have analogues for other Prikry 
 type forcings. The first of these is Mathias' characterization of Prikry s
 equences as those that are almost contained in every set of measure 1 with
  respect to the normal ultrafilter being used for the forcing. This is the
  key to the second property\, which is that the sequence of critical point
 s when forming iterated ultrapowers by that ultrafilter is a Prikry sequen
 ce over the limit model. Using this\, it is not hard to conclude that Prik
 ry sequences are maximal\, in the sense that they almost contain every oth
 er Prikry sequence present in their forcing extension. Another phenomenon 
 is that the forcing extension of the limit model by the critical sequence 
 is the same as the intersection of the finite iterates. I will show anothe
 r canonical representation of that model. Yet another property is that the
  limit model can be realized as a single Boolean ultrapower. Most of these
  results were known for Prikry forcing\, and I will show that some of them
  carry over to certain variants of Prikry forcing and Magidor forcing.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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