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.
Citation
Natasha Dobrinen. Stevo Todorcevic. "Tukey types of ultrafilters." Illinois J. Math. 55 (3) 907 - 951, Fall 2011. https://doi.org/10.1215/ijm/1369841791
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