We identify the class of
–inductive sets studied by Moschovakis as a set theoretical generalization of the class (1,3) of the Rabin-Mostowski index hierarchy of alternating automata on infinite trees. That is, we show that every tree language recognized by an alternating automaton of index (1,3) is
–inductive, and exhibit an automaton whose language is complete in this class w.r.t. continuous reductions.