TY - JOUR
T1 - Reasonable ultrafilters, again
AU - Roslanowski, Andrzej
AU - Shelah, Saharon
PY - 2011
Y1 - 2011
N2 - We continue investigations of reasonable ultrafilters on uncountable cardinals defined in previous work by Shelah. We introduce stronger properties of ultrafilters and we show that those properties may be handled in λ-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal λ with generating systems of size less than 2 λ. We also show how ultrafilters generated by small systems can be killed by forcing notions which have enough reasonable completeness to be iterated with λ-supports.
AB - We continue investigations of reasonable ultrafilters on uncountable cardinals defined in previous work by Shelah. We introduce stronger properties of ultrafilters and we show that those properties may be handled in λ-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal λ with generating systems of size less than 2 λ. We also show how ultrafilters generated by small systems can be killed by forcing notions which have enough reasonable completeness to be iterated with λ-supports.
KW - Iterated forcing
KW - Reasonable ultrafilters
UR - http://www.scopus.com/inward/record.url?scp=79960156090&partnerID=8YFLogxK
U2 - 10.1215/00294527-1306154
DO - 10.1215/00294527-1306154
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AN - SCOPUS:79960156090
SN - 0029-4527
VL - 52
SP - 113
EP - 147
JO - Notre Dame Journal of Formal Logic
JF - Notre Dame Journal of Formal Logic
IS - 2
ER -