Ramseyan ultrafilters

Volume 169 / 2001

Lorenz Halbeisen Fundamenta Mathematicae 169 (2001), 233-248 MSC: Primary 05D05, 05D10; Secondary 03E05, 03E40, 03E17, 03E35. DOI: 10.4064/fm169-3-3

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.

Authors

  • Lorenz HalbeisenDepartment of Pure Mathematics
    Queen's University Belfast
    Belfast BT7 1NN, Northern Ireland
    e-mail

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