Analytic inductive definitions
Douglas Cenzer · Journal of Symbolic Logic · 1974
An operator Γ mapping P(ω) to itself is inductive if Γ(A) ⊇ A for all A. For such an inductive operator Γ we define {Γα: α ∈ ORD} by letting Γ = ⌀, Γα + 1 = Γ(Γα) for all α, and Γβ = ⋃{Γα: α 1 (the latter by definition).