The P-hierarchy of ultrafilters

Seminar
Speaker
Michal Machura (BIU)
Date
14/12/2014 - 12:00 - 10:15Add to Calendar 2014-12-14 10:15:00 2014-12-14 12:00:00 The P-hierarchy of ultrafilters 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 ℵ1 disjoint classes P(α) where α is ordinal number <ω1. The class P(1) is just a class of principal ultrafilters. The class P(2) is composed of P-points,  which were isolated by Rudin in order to prove non-homogeneity 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(α) of P-hierarchy and other special types of ultrafilters, including: Baumgartner’s I-ultrafilters, thin ultrafilters, summable ultrafilters, and van der Waerden ultrafilters. אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
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 ℵ1 disjoint classes P(α) where α is ordinal number <ω1. The class P(1) is just a class of principal ultrafilters. The class P(2) is composed of P-points,  which were isolated by Rudin in order to prove non-homogeneity 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(α) of P-hierarchy and other special types of ultrafilters, including: Baumgartner’s I-ultrafilters, thin ultrafilters, summable ultrafilters, and van der Waerden ultrafilters.

תאריך עדכון אחרון : 10/12/2014