Sh:890

• Rosłanowski, A., & Shelah, S. (2011). Reasonable ultrafilters, again. Notre Dame J. Form. Log., 52(2), 113–147. arXiv: math/0605067 DOI: 10.1215/00294527-1306154 MR: 2794647
• Abstract:
  We continue investigations of reasonable ultrafilters on uncountable cardinals defined in [Sh:830]. 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).
• Version 2010-09-20_11 (33p) published version (35p)

@article{Sh:890,
 author = {Ros{\l}anowski, Andrzej and Shelah, Saharon},
 title = {{Reasonable ultrafilters, again}},
 journal = {Notre Dame J. Form. Log.},
 fjournal = {Notre Dame Journal of Formal Logic},
 volume = {52},
 number = {2},
 year = {2011},
 pages = {113--147},
 issn = {0029-4527},
 mrnumber = {2794647},
 mrclass = {03E35 (03E05 03E20)},
 doi = {10.1215/00294527-1306154},
 note = {\href{https://arxiv.org/abs/math/0605067}{arXiv: math/0605067}},
 arxiv_number = {math/0605067}
}