Notre Dame Journal of Formal Logic

Reasonable Ultrafilters, Again

Andrzej Rosłanowski and Saharon Shelah


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.

Article information

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

First available in Project Euclid: 28 April 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E35: Consistency and independence results
Secondary: 03E05: Other combinatorial set theory 03E20: Other classical set theory (including functions, relations, and set algebra)

reasonable ultrafilters iterated forcing


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

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