Andrzej Starosolski: The Rudin-Keisler ordering of P-points under b=c

Tuesday, May 15, 2018, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Andrzej Starosolski (Silesian University of Technology)

Title: The Rudin-Keisler ordering of P-points under $\mathfrak b=\mathfrak c$


M. E. Rudin proved under CH that for each P-point there exists another P-point strictly RK-greater . Assuming $\mathfrak p=\mathfrak c$, A. Blass showed the same; moreover, he proved that each RK-increasing $\omega$-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-preordering. He also asked what ordinals can be embedded in the set of P-points.
In my talk the results cited above are proved and the mentioned question is answered under a (weaker) assumption $\mathfrak b =\mathfrak c$.

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