Andrzej Starosolski

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

    Authors: Michał Machura, Andrzej Starosolski
    Subjects: Logic
    Abstract

    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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