Ramseyan ultrafilters

Lorenz Halbeisen. "Ramseyan ultrafilters." Fundamenta Mathematicae 169.3 (2001): 233-248. <http://eudml.org/doc/282235>.

@article{LorenzHalbeisen2001,
abstract = {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.},
author = {Lorenz Halbeisen},
journal = {Fundamenta Mathematicae},
keywords = {dual Ramsey theory; partitions; filters; happy families; Mathias forcing},
language = {eng},
number = {3},
pages = {233-248},
title = {Ramseyan ultrafilters},
url = {http://eudml.org/doc/282235},
volume = {169},
year = {2001},
}

TY - JOUR
AU - Lorenz Halbeisen
TI - Ramseyan ultrafilters
JO - Fundamenta Mathematicae
PY - 2001
VL - 169
IS - 3
SP - 233
EP - 248
AB - 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.
LA - eng
KW - dual Ramsey theory; partitions; filters; happy families; Mathias forcing
UR - http://eudml.org/doc/282235
ER -