Journal of Symbolic Logic

The Rudin-Blass Ordering of Ultrafilters

Claude Laflamme and Jian-Ping Zhu

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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.

Article information

Source
J. Symbolic Logic, Volume 63, Issue 2 (1998), 584-592.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745522

Mathematical Reviews number (MathSciNet)
MR1627310

Zentralblatt MATH identifier
0911.04001

JSTOR
links.jstor.org

Citation

Laflamme, Claude; Zhu, Jian-Ping. The Rudin-Blass Ordering of Ultrafilters. J. Symbolic Logic 63 (1998), no. 2, 584--592. https://projecteuclid.org/euclid.jsl/1183745522


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