Reasonable ultrafilters, again
Logic
2013-01-04 v2
Abstract
We continue investigations of reasonable ultrafilters on uncountable cardinals defined in math.LO/0407498. We introduce stronger properties of ultrafilters and we show that those properties may be handled in lambda-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal lambda with generating system of size less than 2^lambda . We also show how reasonable ultrafilters can be killed by forcing notions which have enough reasonable completeness to be iterated with lambda-supports (and we show the appropriate preservation theorem).
Keywords
Cite
@article{arxiv.math/0605067,
title = {Reasonable ultrafilters, again},
author = {Andrzej Roslanowski and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0605067},
year = {2013}
}