In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is \\D
Using transfinite recursion, we shall construct an ordinal-indexed sequence ⟨xα⟩ of members of [a, b] such that every ordinal α has the following properties: The function f is bounded on [a, xα]. We have xα ≤ xα + 1, and if xα = xα + 1, ...