Ramseyan ultrafilters

• Autorzy: Lorenz Halbeisen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E40: Other aspects of forcing and Boolean-valued models
• 03E05: Other combinatorial set theory
• 05D10: Ramsey theory
• 05D05: Extremal set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 169
• Numer: 3
• Strony: 233-248

Daty

wydano

2001

Twórcy

autor

Lorenz Halbeisen

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

Identyfikatory

DOI

10.4064/fm169-3-3