**"Ultrafilters and Ideal Independent Families"**
#### Switzer, CoreyA family $\mathcal I \subseteq [\omega]^\omega$ is called ideal independent if for every $A \in \mathcal I$ and every finite $F \subseteq \mathcal I \setminus \{A\}$ we have $A \nsubseteq^* \bigcup F$. In other words $A$ is not in the ideal generated by $\mathcal I \setminus \{A\}$. The cardinal $\mathfrak{s}_{mm}$ is defined as the minimal size a of a maximal ideal independent family. In this talk we will discuss how this cardinal relates to other cardinal characteristics of extremal sets of reals. In particular we will show that $\mathfrak{s}_{mm}$ is independent the independence number $\mathfrak{i}$, but surprisingly, $\mathsf{ZFC}$-provably greater than or equal to the ultrafilter number $\mathfrak{u}$. This is joint work with Jonathan Cancino and Vera Fischer. |