Journal of Symbolic Logic

The Rudin-Blass Ordering of Ultrafilters

Claude Laflamme and Jian-Ping Zhu

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.


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

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

First available in Project Euclid: 6 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Laflamme, Claude; Zhu, Jian-Ping. The Rudin-Blass Ordering of Ultrafilters. J. Symbolic Logic 63 (1998), no. 2, 584--592.

Export citation