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The Rudin-Blass Ordering of Ultrafilters

Claude Laflamme and Jian-Ping Zhu
The Journal of Symbolic Logic
Vol. 63, No. 2 (Jun., 1998), pp. 584-592
DOI: 10.2307/2586852
Stable URL: http://www.jstor.org/stable/2586852
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Rudin-Blass Ordering of Ultrafilters
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Abstract

We discuss the finite-to-one Rudin-Keisler ordering of ultrafilters on the natural numbers, which we baptize the Rudin-Blass ordering in honour of Professor Andreas Blass who worked extensively in the area. We develop and summarize many of its properties in relation to its bounding and dominating numbers, directedness, and provide applications to continuum theory. In particular, we prove in ZFC alone that there exists an ultrafilter with no Q-point below in the Rudin-Blass ordering.

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