Reasonable Ultrafilters, Again

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

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Citations of this work

Fusion and Large Cardinal Preservation.Sy-David Friedman, Radek Honzik & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (12):1247-1273.
A Parallel to the Null Ideal for Inaccessible $$\lambda $$ Λ : Part I.Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (3-4):319-383.

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References found in this work

Set Theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
On Non-Minimal P-Points Over a Measurable Cardinal.Moti Gitik - 1981 - Annals of Mathematical Logic 20 (3):269-288.
Ramsey Ultrafilters and the Reaping Number—Con(R.M. Goldstern & S. Shelah - 1990 - Annals of Pure and Applied Logic 49 (2):121-142.
Generating Ultrafilters in a Reasonable Way.Andrzej Rosłanowski & Saharon Shelah - 2008 - Mathematical Logic Quarterly 54 (2):202-220.

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