Agrawal et al. used their equivalence between AC0 reductions and NC0 reductions to show that all sets complete for NP under AC0 reductions are AC0-isomorphic.
Agrawal et al. leveraged their relationship between AC0 reductions and NC0 reductions to prove that all sets that can be completed in polynomial time under AC0 reductions are isomorphic within the class of AC0 reductions.