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Happy Families and Their Relatives

Thursday 27th August 2015 - 11:30 to 12:30
INI Seminar Room 1
We first recall the notion of $\ happy$$\ families$ as well as their combinatorial properties. Then we present some families which are related to $\ happy$$\ families$ and investigate $\ Mathias$$\ forcing$ restricted to these families. In the second part we show the relation between $\it Mathias$$\ forcing$ and the $\ Ramsey$$\ property$ and discuss the still open problem whether one can take $\ Mathias'$$\ inaccessible$ away. In the last part, we sketch Shelah's construction of a model of ZFC in which there are exactly $\ 70$$\ happy$$\ ultrafilters$.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons