Reasonable Ultrafilters, Again

Notre Dame Journal of Formal Logic 52 (2):113-147 (2011)

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
Keywords reasonable ultrafilters   iterated forcing
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DOI 10.1215/00294527-1306154
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References found in this work BETA

On Non-Minimal P-Points Over a Measurable Cardinal.Moti Gitik - 1981 - Annals of Mathematical Logic 20 (3):269-288.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Proper and Improper Forcing.Saharon Shelah - 2000 - Bulletin of Symbolic Logic 6 (1):83-86.

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Citations of this work BETA

Fusion and Large Cardinal Preservation.Sy-David Friedman, Radek Honzik & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (12):1247-1273.

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