2001/09/16 by Lorenz Halbeisen
Mathematics · #math.LO #msc:05D05 #msc:05D10 #msc:03E05 #msc:03E40 #msc:03E17 #msc:03E35
published as Fundamenta Mathematicae 169 (2001) 233-248
arxiv created 2001/09/16 · arxiv updated 2009/11/30
We investigate families of partitions of omega which are related to special coideals, so-called happy families, and give a dual form of Ramsey ultrafilters in terms of partitions. The combinatorial properties of these partition-ultrafilters, which we call Ramseyan ultrafilters, are similar to those of Ramsey ultrafilters. For example it will be shown that dual Mathias forcing restricted to a Ramseyan ultrafilter has the same features as Mathias forcing restricted to a Ramsey ultrafilter. Further we introduce an ordering on the set of partition-filters and consider the dual form of some cardinal characteristics of the continuum.