## Notre Dame Journal of Formal Logic

### Reasonable Ultrafilters, Again

#### Abstract

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 $2^\lambda$. 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.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 52, Number 2 (2011), 113-147.

Dates
First available in Project Euclid: 28 April 2011

https://projecteuclid.org/euclid.ndjfl/1303995710

Digital Object Identifier
doi:10.1215/00294527-1306154

Mathematical Reviews number (MathSciNet)
MR2794647

Zentralblatt MATH identifier
1232.03034

#### Citation

Rosłanowski, Andrzej; Shelah, Saharon. Reasonable Ultrafilters, Again. Notre Dame J. Formal Logic 52 (2011), no. 2, 113--147. doi:10.1215/00294527-1306154. https://projecteuclid.org/euclid.ndjfl/1303995710