The Rudin-Blass ordering of ultrafilters

Journal of Symbolic Logic 63 (2):584-592 (1998)
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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



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References found in this work

Forcing with Filters and Complete Combinatorics.Claude Laflamme - 1989 - Annals of Pure and Applied Logic 42 (2):125-163.
Near Coherence of Filters. I. Cofinal Equivalence of Models of Arithmetic.Andreas Blass - 1986 - Notre Dame Journal of Formal Logic 27 (4):579-591.
Cofinalities of Countable Ultraproducts: The Existence Theorem.R. Michael Canjar - 1989 - Notre Dame Journal of Formal Logic 30 (4):539-542.

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