The algebraic numbers definable in various exponential fields
  We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular $\mathbb C$ or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: For the Zilber fields, the only pointwise definable algebraic numbers are the real abelian numbers. 
Jonathan Kirby, Angus Macintyre, and Alf Onshuus
math.LO math.NT