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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
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2586852
Page Count: 9
You can always find the topics here!Topics: Ultrafilters, Mathematical functions, Mathematical theorems, Mathematical monotonicity, Increasing functions, Natural numbers, Monotonic functions, Cofinality, Logical theorems, General topology
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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.
The Journal of Symbolic Logic © 1998 Association for Symbolic Logic