We investigate families of partitions of ω 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-3-3,
author = {Lorenz Halbeisen},
title = {Ramseyan ultrafilters},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {233-248},
zbl = {0982.03026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-3-3}
}
Lorenz Halbeisen. Ramseyan ultrafilters. Fundamenta Mathematicae, Tome 167 (2001) pp. 233-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-3-3/