Illinois Journal of Mathematics

Tukey types of ultrafilters

Natasha Dobrinen and Stevo Todorcevic

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 29 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1369841791

Digital Object Identifier
doi:10.1215/ijm/1369841791

Mathematical Reviews number (MathSciNet)
MR3069290

Zentralblatt MATH identifier
1291.03083

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

Citation

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


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