Tukey types of ultrafilters

Details Tukey types of ultrafilters Tukey types of ultrafilters

2011-10-19

arxiv.org/abs/1110.4153v1

Mathematics

Logic

33 pages, to appear in 2012 in the Illinois Journal of Mathematics

Scientific paper

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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