Tukey types of ultrafilters

By Natasha Dobrinen, Stevo Todorcevic. 2011

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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.

Subfields: Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cd2cc7d1c38d2dc1947688298634ea73cfac1f2e