Reducts of the Generic Digraph

The generic digraph (D, E) is the unique countable homogeneous digraph that embeds all finite digraphs. In this paper, we determine the lattice of reducts of (D, E), where a structure M is a reduct of (D, E) if it has domain D and all its ∅-definable relations are ∅-definable relations of (D, E). As (D, E) is ℵ0-categorical, this is equivalent to determining the lattice of closed groups that lie in between Aut(D, E) and Sym(D).