# Happy Families and Their Relatives

Presented by:
L J Halbeisen ETH Zürich
Date:
Thursday 27th August 2015 - 11:30 to 12:30
Venue:
INI Seminar Room 1
Abstract:
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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