Geodesic
Ramseyan ultrafilters
Lorenz Halbeisen1
1 Department of Pure Mathematics Queen's University Belfast Belfast BT7 1NN, Northern Ireland
Fundamenta Mathematicae, Tome 169 (2001) no. 3, pp. 233-248

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm169-3-3
Keywords: investigate families partitions omega which related special coideals so called happy families dual form ramsey ultrafilters terms partitions combinatorial properties these partition ultrafilters which call ramseyan ultrafilters similar those ramsey ultrafilters example shown dual mathias forcing restricted ramseyan ultrafilter has features mathias forcing restricted ramsey ultrafilter further introduce ordering set partition filters consider dual form cardinal characteristics continuum

Lorenz Halbeisen 1

1 Department of Pure Mathematics Queen's University Belfast Belfast BT7 1NN, Northern Ireland 
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Lorenz Halbeisen. Ramseyan ultrafilters. Fundamenta Mathematicae, Tome 169 (2001) no. 3, pp. 233-248. doi: 10.4064/fm169-3-3

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