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

Michał Machura, Andrzej Starosolski

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 cla…