Independent families in the countable and the uncountable

Seminar
Speaker
Vera Fischer (Vienna)
Date
18/11/2020 - 16:00 - 14:00Add to Calendar 2020-11-18 14:00:00 2020-11-18 16:00:00 Independent families in the countable and the uncountable Independent families on $\omega$ are families of infinite sets of integers with the property that for any two finite subfamilies $A$ and $B$ the set $\bigcap A\backslash \bigcup B$ is infinite. Of particular interest are the sets of the possible cardinalities of maximal independent families, which we refer to as the spectrum of independence. Even though we do have the tools to control the spectrum of independence at $\omega$ (at least to a  large extent), there are many relevant questions regarding higher counterparts of independence in generalised Baire spaces, which remain widely open. Zoom אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Zoom
Abstract

Independent families on $\omega$ are families of infinite sets of integers with the property that for any two finite subfamilies $A$ and $B$ the set $\bigcap A\backslash \bigcup B$ is infinite. Of particular interest are the sets of the possible cardinalities of maximal independent families, which we refer to as the spectrum of independence. Even though we do have the tools to control the spectrum of independence at $\omega$ (at least to a  large extent), there are many relevant questions regarding higher counterparts of independence in generalised Baire spaces, which remain widely open.

Last Updated Date : 14/11/2020