A definable $\mathsf E_0$-class containing no definable elements
  A generic extension $L[x]$ of $L$ by a real $x$ is defined, in which the $\mathsf E_0$-class of $x$ is a lightface $\Pi^1_2$ set containing no ordinal-definable reals. 
Vladimir Kanovei and Vassily Lyubetsky
math.LO