منابع مشابه
Tukey Types of Ultrafilters
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, ...
متن کاملSpectra of Tukey Types of Ultrafilters on Boolean Algebras
Extending recent investigations on the structure of Tukey types of ultrafilters on P(ω) to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras. These include the classes of free Boolean algebras, superatomic Boolean algebras generated by almost disjoint families, interval algebras, tree algebras, and pseudo-tree algebras. W...
متن کاملTukey Classes of Ultrafilters on Ω
Motivated by a question of Isbell, we show that ♦ implies there is a non-P-point U ∈ βω \ ω such that neither 〈U ,⊇〉 nor 〈U ,⊇∗〉 is Tukey equivalent to 〈[c],⊆〉. We also show that 〈U ,⊇∗〉 ≡T 〈[c] ,⊆〉 for some U ∈ βω \ ω, assuming cf(κ) = κ ≤ p = c. We also prove two negative ZFC results about the possible Tukey classes of ultrafilters on ω.
متن کاملSurvey on the Tukey Theory of Ultrafilters
This article surveys results regarding the Tukey theory of ultrafilters on countable base sets. The driving forces for this investigation are Isbell’s Problem and the question of how closely related the Rudin-Keisler and Tukey reducibilities are. We review work on the possible structures of cofinal types and conditions which guarantee that an ultrafilter is below the Tukey maximum. The known ca...
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Motivated by a question of Isbell, we show that ♦ implies there is a non-P-point U ∈ βω \ ω such that neither 〈U ,⊇〉 nor 〈U ,⊇∗〉 is Tukey equivalent to 〈[c],⊆〉. We also show that 〈U ,⊇∗〉 ≡T 〈[c],⊆〉 for some U ∈ βω \ ω, assuming cf(κ) = κ ≤ p = c. We also prove two negative ZFC results about the possible Tukey classes of ultrafilters on ω.
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2011
ISSN: 0019-2082
DOI: 10.1215/ijm/1369841791