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

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

2011-08-08

arxiv.org/abs/1108.1818v4

Mathematics

Logic

17 pages, rewritted

Scientific paper

Under CH we prove that for any tall ideal $\cal I$ on $\omega$ and for any ordinal $\gamma \leq \omega_1$ there is an ${\cal I}$-ultrafilter (in the sense of Baumgartner), which belongs to the class ${\cal P}_{\gamma}$ of P-hierarchy of ultrafilters. Since the class of ${\cal P}_2$ ultrafilters coincides with a class of P-points, out result generalize theorem of Fla\v{s}kov\'a, which states that there are ${\cal I}$-ultrafilters which are not P-points.

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