Definable maximal cofinitary groups
  Using countable support iteration of $S$-proper posets, for some appropriate stationary set $S$, we obtain a generic extension of the constructible universe, in which $\mathfrak{b}=\mathfrak{c}=\aleph_2$ and there is a maximal cofinitary group with a $\Pi^1_2$-definable set of generators. 
Vera Fischer, Sy David Friedman, Asger T\"ornquist
math.LO