Authors: | Dobrinen, Natasha Todorčević, Stevo |
Title: | Tukey types of ultrafilters |
Journal: | Illinois Journal of Mathematics |
Volume: | 55 |
Issue: | 3 |
First page: | 907 |
Last page: | 951 |
Issue Date: | 1-Dec-2011 |
Rank: | M23 |
ISSN: | 0019-2082 |
DOI: | 10.1215/ijm/1369841791 |
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. |
Publisher: | University of Illinois |
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