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Tukey types of ultrafilters. (English) Zbl 1291.03083

Summary: 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.

MSC:

03E05 Other combinatorial set theory
03E17 Cardinal characteristics of the continuum
03E35 Consistency and independence results
06A07 Combinatorics of partially ordered sets
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References:

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