The Rudin–Keisler ordering of P-points under b = c

Speaker(s)

Andrzej Starosolski

Affiliation

Silesian University of Technology

Date

Dec. 5, 2018, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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M. E. Rudin (1971) proved, under CH, that for each P-point there exists a P-point strictly RK-greater. This result was proved under p = c by A. Blass (1973), who also showed that each RK-increasing ω-sequence of P-points is upper bounded by a P-point, and that there is an order embedding of the real line into the class of P-points with respect to the RK-ordering. In this presentation, the results cited above, with addition of embedding of a long-line into P-points are proved under the (weaker) assumption that b = c.
A. Blass asked in 1973 which ordinals can be embedded in the set of P-points, and pointed out that such an ordinal cannot be greater then c^+. We proved (under b = c) that each ordinal less then c^+ may be embedded  into P-points.
These resuts can be found in the preprint: https://arxiv.org/abs/1803.03862

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