# Bounding, splitting and almost disjointness can be quite different

## Vera Fischer

### Kurt Godel Research Center

The bounding, splitting and almost disjoint families are some of the well studied infinitary combinatorial objects on the real line. Their study has prompted the development of many interesting forcing techniques. Among those are the method of creature forcing, as well as Shelah’s template iteration techniques.

In this talk, we will discuss some recent developments of Shelah’s template iteration methods, leading to models in which the bounding, the splitting and the almost disjointness numbers can be quite arbitrary. We will conclude with a brief discussion of open problems.

Vera Fischer completed her doctorate in 2008 at York University, under the supervision of Juris Steprans, and now is an assistant at the Kurt GĂ¶del Research Center in Vienna. She studies combinatorial set theory, the structure of the real line, and forcing.