Abstract: 
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.

1. Department of Pure Mathematics
   Queen's University Belfast
   Belfast BT7 1NN, Northern Ireland