Open Access
2011 Reasonable Ultrafilters, Again
Andrzej Rosłanowski, Saharon Shelah
Notre Dame J. Formal Logic 52(2): 113-147 (2011). DOI: 10.1215/00294527-1306154


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.


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Andrzej Rosłanowski. Saharon Shelah. "Reasonable Ultrafilters, Again." Notre Dame J. Formal Logic 52 (2) 113 - 147, 2011.


Published: 2011
First available in Project Euclid: 28 April 2011

zbMATH: 1232.03034
MathSciNet: MR2794647
Digital Object Identifier: 10.1215/00294527-1306154

Primary: 03E35
Secondary: 03E05 , 03E20

Keywords: Iterated forcing , reasonable ultrafilters

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 2 • 2011
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