The Journal of Symbolic Logic

Research Article

The Rudin-Blass ordering of ultrafilters

Claude Laflammea1 and Jian-Ping Zhua2

a1 Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4, E-mail: laflamme@acs.ucalgary.ca

a2 Versus Technologies Inc., 181 Bay Street, Suite 3810, Toronto, Canada M5J 2T3, E-mail: jzhu@tradeit.com

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.

(Received July 07 1996)

(Revised January 19 1997)