How high can Baumgartner's {\cal I}-ultrafilters lie in the P-hierarchy?

Abstract

Under CH we prove that for any tall ideal $\mathcal{I}$ on $\omega$ and for any ordinal $\gamma \le {\omega }_1$ there is an $\mathcal{I}$-ultrafilter (in the sense of Baumgartner), which belongs to the class ${\mathcal{P}}_{\gamma }$ of P-hierarchy of ultrafilters. Since the class of ${\mathcal{P}}_2$ ultrafilters coincides with a class of P-points, out result generalize theorem of Flašková, which states that there are $\mathcal{I}$-ultrafilters which are not P-points.

17 pages, rewritted

Cited by in corpus (1)

• Rudin-Kisler ordering on the P-hierarchy