On embedding certain partial orders into the P-points under Rudin-Keisler and Tukey reducibility

The Rudin-keisler Ordering of F-points

On Rudin–keisler Preorders in Small Theories

We consider complete first-order theories T with infinite models. Additionally we assume that T are small, i. e., they have countably many types (|S(T )| = ω). So for any type q ∈ S(T ) and its realization ā, there exists a model M(ā), being prime over ā. Since all prime models over realizations of q are isomorphic, we often denote such by Mq. Let p and q be types in S(T ). We say that the type...

Cofinal types of ultrafilters

We study Tukey types of ultrafilters on ω, focusing on the question of when Tukey reducibility is equivalent to Rudin-Keisler reducibility. We give several conditions under which this equivalence holds. We show that there are only c many ultrafilters that are Tukey below any basically generated ultrafilter. The class of basically generated ultrafilters includes all known ultrafilters that are n...

A Remark on the Rudin-keisler Order of Ultrafilters

Define a (pre)order on /3co as follows: p • q iff there is a finite to one function f c woo such that/3f(cl) = p. Let ,•{ denote he Rudin-Keisler order on Ow. We show that here are points p,qCw* such that Px•q, but p and q are •<-incomparable. 0. Introduction. In [5], M. E. Rudin showed that if there are points p,q G co* Such that for any finite to one function f G cow we have that 13f(p) 4:13f...

Rudin-Keisler Posets of Complete Boolean Algebras

The Rudin-Keisler ordering of ultrafilters is extended to complete Boolean algebras and characterised in terms of elementary embeddings of Boolean ultrapowers. The result is applied to show that the Rudin-Keisler poset of some atomless complete Boolean algebras is nontrivial.