Cofinal types of ultrafilters |
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Authors: | Dilip Raghavan Stevo Todorcevic |
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Institution: | a Graduate School of System Informatics, Kobe University, Rokko-dai 1-1, Nada KOBE 657-8501, Japanb Department of Mathematics, University of Toronto, 40 St George St Toronto, ON M5S 2E4, Canada |
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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 ω1]<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. |
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Keywords: | 03E04 03E05 03E35 54A20 |
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