Authors: Raghavan, Dilip
Todorčević, Stevo 
Title: Cofinal types of ultrafilters
Journal: Annals of Pure and Applied Logic
Volume: 163
Issue: 3
First page: 185
Last page: 199
Issue Date: 1-Mar-2012
Rank: M22
ISSN: 0168-0072
DOI: 10.1016/j.apal.2011.08.002
We study Tukey types of ultrafilters on ω, focusing on the question of when Tukey reducibility is equivalent to Rudin-Keisler reducibility. We give several conditions under which this equivalence holds. We show that there are only c many ultrafilters that are Tukey below any basically generated ultrafilter. The class of basically generated ultrafilters includes all known ultrafilters that are not Tukey above [ω 1] <ω. We give a complete characterization of all ultrafilters that are Tukey below a selective. A counterexample showing that Tukey reducibility and RK reducibility can diverge within the class of P-points is also given.
Keywords: Cofinal type | Rudin-Keisler order | Tukey reducibility | Ultrafilter
Publisher: Elsevier

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