# 2019 seminar talk: Cichoń's Maximum without large cardinals

Talk held by Martin Goldstern (TU Wien) at the KGRC seminar on 2019-11-21.

### Abstract

How many Lebesgue null sets are needed to cover the real line? How many functions (from the natural numbers to the natural numbers) are needed to dominate all functions? The answers to these questions and 10 more related questions are certain uncountable cardinals collected in Cichoń's Diagram, which also shows provable inequalities between these cardinals.

In a recent joint work with Jakob Kellner, Diego Mejía and Saharon Shelah, we constructed a model where the cardinals in Cichoń's Diagram have 10 different values (which is known to be best possible).

The construction first uses a finite support iteration P to get 5 different values for the left side of the diagram, and then finds a subset P' which also separates the values on the right side.