# 2015 seminar talk: Separating the left side of Cichon's diagram

Talk held by Diego Alejandro Mejía Guzmán (TU Wien) at the KGRC seminar on 2015-11-05.

### Abstract

It is well known that, with finite support iterations of ccc posets, we can obtain models where 3 or more cardinals of Cichon's diagram can be separated. For example, concerning the left side of Cichon's diagarm, it is consistent that $\aleph_1 < add(N) < cov(N) < b < non(M)=cov(M)=c$. Nevertheless, getting the additional strict inequality $non(M) < cov(M)$ is a challenge because subposets of $E$, the standard ccc poset that adds an eventually different real, may add dominating reals (by Pawlikowski, 1992).

We construct a model of $\aleph_1 < add(N) < cov(N) < b < non(M) < cov(M)=c$ with the help of chains of ultrafilters that allows to preserve certain unbounded families.

This is a joint work with M. Goldstern and S. Shelah.