Journal of Symbolic Logic

Some Initial Segments of the Rudin-Keisler Ordering

Andreas Blass

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Abstract

A 2-affable ultrafilter has only finitely many predecessors in the Rudin-Keisler ordering of isomorphism classes of ultrafilters over the natural numbers. If the continuum hypothesis is true, then there is an $\aleph_1$-sequence of ultrafilters $D_\alpha$ such that the strict Rudin-Keisler predecessors of $D_\alpha$ are precisely the isomorphs of the $D_\beta$'s for $\beta < \alpha$.

Article information

Source
J. Symbolic Logic, Volume 46, Issue 1 (1981), 147-157.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183740728

Mathematical Reviews number (MathSciNet)
MR604888

Zentralblatt MATH identifier
0463.03027

JSTOR
links.jstor.org

Citation

Blass, Andreas. Some Initial Segments of the Rudin-Keisler Ordering. J. Symbolic Logic 46 (1981), no. 1, 147--157. https://projecteuclid.org/euclid.jsl/1183740728


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