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 | Abstract: | 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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