# Coherent Systems of Finite Support Iterations

## Vera Fischer

### Kurt Godel Research Center

The method of matrix iterations was introduced by Blass and Shelah in their study of the dominating and the ultrafilter numbers. Since its appearance, the method has undergone significant development and applied to the study of many other cardinal characteristics of the continuum, including those associated to measure and category.

Recently, we were able to extend the technique of matrix iterations to a “third dimension” and so, evaluate the almost disjointness number in models where previously its value was not known. In addition, we obtain new constellations of the Cichon diagram (with up to seven distinct values). This is a joint work with Friedman, Mejia and Montoya.

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.