**March 25**

**Vera Fischer**,
University of Vienna

**Independent families, Spectra and Indestructibility**

Independent families are families of infinite sets of integers with the property that for any two disjoint, non-empty, finite subfamilies $A$ and $B$ of the given family, the set $\bigcap A\backslash \bigcup B$ is infinite. Of particular interest are the sets of the possible cardinalities of maximal independent families, as well as their indestructibility by various forcing notions. In this talk, we will consider some recent advances in the area and point out to remaining open questions.