# Dilip Raghavan: More about the closed almost-disjointness number

12/October/2012, 13:30–15:00
Fields institute,Room 230

Speaker: Dilip Raghavan

Title: More about the closed almost-disjointness number

Abstract: ${\mathfrak{a}}_{\text{closed}}$ is the least $\kappa$ such that there exist $\kappa$-closed subsets of ${[\omega]}^{\omega}$ whose union is a MAD family in ${[\omega]}^{\omega}$. This cardinal invariant was recently introduced by Brendle and Khomskii in connection with the possible descriptive complexities of MAD families in forcing extensions of $\mathbf{L}$.
I will present some recent results on this cardinal invariant. In particular, I will show the consistency of $\mathfrak{b} < {\mathfrak{a}}_{\text{closed}}$. This is joint work with Brendle.