# 2008 seminar talk: Further combinatorial properties of Cohen forcing

Talk held by Vera Fischer (KGRC) at the KGRC seminar on 2008-11-27.

### Abstract

Relaying on some combinatorial properties of Cohen forcing, we suggest a generalization of Mathias forcing which preserves the unboundedness of small unbounded families. The construction can be considered a first step towards obtaining the consistency of $\omega_1< \mathfrak{b}<\mathfrak{b}^+<\mathfrak{s}$.