Some initial segments of the Rudin-Keisler ordering

Journal of Symbolic Logic 46 (1):147-157 (1981)
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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 ℵ 1 -sequence of ultrafilters D α such that the strict Rudin-Keisler predecessors of D α are precisely the isomorphs of the D β 's for $\beta

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Forcing with filters and complete combinatorics.Claude Laflamme - 1989 - Annals of Pure and Applied Logic 42 (2):125-163.

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