A Colloquium in Mathematics , The P-hierarchy of ultrafilters

The Faculty of Sciences, A Colloquium in Mathematics:

The P-hierarchy of ultrafilters

Dr. Michael Machura, Bar-Ilan University

Sunday, 2 November 2014 | 15:00 | Science Building (8), Room 424

On the talk, we shall present a P-hierarchy of ultrafilters, that was invited 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. On the 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, van der Waerden ultrafilters.

For further information: David Garber, Department of Applied Mathematics, Faculty of Sciences, Holon Institute of Technology

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