Michal Machura: The P-hierarchy of ultrafilters

Infinite Combinatorics Seminar (BIU)

14/December/2014, 10:15-12:00,
Room 201, Building 216, Bar-Ilan University

Speaker: Michal Machura (BIU)

Title: The P-hierarchy of ultrafilters

Abstract: We shall present the P-hierarchy of ultrafilters, that was posed by Andrzej Starosolski.
The P-hierarchy of ultrafilters is one of many ways to classify ultrafilters on natural numbers and it is composed of $\aleph_1$  disjoint classes $P_{\alpha}$ where $\alpha$ is ordinal number $<\omega_1$. The class $P_{1}$ is just a class of principal ultrafilters. The class $P_{2}$ is composed of  P-points,  which were defined by Rudin in order to prove non-homogenity of the remainder of Cech-Stone compactification of natural numbers. Next, in higher classes of P-hierarchy, one can find ultrafilters with more and more complicated structures.
In this talk, we will disscuss relations between classes $P_{\alpha}$ of P-hierarchy and other special types of ultrafilters like: Baumgartner’s I-ultrafilters, thin ultrafilters, summable ultrafilters, and van der Waerden ultrafilters.

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