Tukey types of ultrafilters

Natasha Dobrinen; Stevo Todorcevic

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arXiv · 1110.4153

Tukey types of ultrafilters

Natasha Dobrinen·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.

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BibTeX RIS

Natasha Dobrinen, Stevo Todorcevic. 2011-10-19. Tukey types of ultrafilters. https://arxiv.org/abs/1110.4153

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