English

Ramseyan ultrafilters

Logic 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0109102,
  title  = {Ramseyan ultrafilters},
  author = {Lorenz Halbeisen},
  journal= {arXiv preprint arXiv:math/0109102},
  year   = {2007}
}