# Algebra Seminar talk

2019-10-18

Martin **Goldstern***Cichoń's Diagram and set-theoretic universes*

Abstract:

In part 1 of my talk, I described
Cichoń's Diagram, which describes a partial order between 10 uncountable cardinals,
among them

- cov(null) = the smallest number of Lebesgue null sets needed to cover all real numbers,
- non(meager) = the smallest cardinality of a non-meager set (=set of second category),
- as well as aleph1 (smallest uncountable cardinal)
- and c (the cardinality of R, the set of all real numbers).

In this part, I will continue to talk a bit about the cardinals in Cichoń's Diagram and hint at the methods which allow us to control/manipulate their values.

This talk is again aimed at a general mathematical audience, with no prior knowledge of ZFC-models or forcing.