abstract
Ramseyan ultrafilters
Lorenz Halbeisen
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.