Illinois Journal of Mathematics

Tukey types of ultrafilters

Natasha Dobrinen and Stevo Todorcevic

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We investigate the structure of the Tukey types of ultrafilters on countable sets partially ordered by reverse inclusion. A canonization of cofinal maps from a $p$-point into another ultrafilter is obtained. This is used in particular to study the Tukey types of $p$-points and selective ultrafilters. Results fall into three main categories: comparison to a basis element for selective ultrafilters, embeddings of chains and antichains into the Tukey types, and Tukey types generated by block-basic ultrafilters on FIN.

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Illinois J. Math., Volume 55, Number 3 (2011), 907-951.

First available in Project Euclid: 29 May 2013

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Zentralblatt MATH identifier

Primary: 03E05: Other combinatorial set theory 03E17: Cardinal characteristics of the continuum 03E35: Consistency and independence results 06A07: Combinatorics of partially ordered sets


Dobrinen, Natasha; Todorcevic, Stevo. Tukey types of ultrafilters. Illinois J. Math. 55 (2011), no. 3, 907--951. doi:10.1215/ijm/1369841791.

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