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SUMMARY:Happy Families and Their Relatives - Halbeisen\, L J (ETH Zrich)
DTSTART:20150827T103000Z
DTEND:20150827T113000Z
UID:TALK60478@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:We first recall the notion of $ happy$$ families$ as well as t
 heir combinatorial properties. Then we present some families which are rel
 ated to $ happy$$ families$ and investigate $ Mathias$$ forcing$ restricte
 d to these families. In the second part we show \nthe relation between $it
  Mathias$$ forcing$ and the $ Ramsey$$ property$ and discuss the still ope
 n problem whether one can take $ Mathias'$$ inaccessible$ away. In the las
 t part\, we sketch Shelah's construction of a model of ZFC in which there 
 are exactly $ 70$$ happy$$ ultrafilters$.\n
LOCATION:Seminar Room 1\, Newton Institute
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