|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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