Let J be a well-ordered set. A subset J0 of J is said to be inductive if for every α ∈ JTh...

Let J be a well-ordered set. A subset J0 of J is said to be inductive if for every α ∈ J

Theorem (The principle of transfinite induction). If J is a well-ordered set and J0 is an inductive subset of J, then J0 = J.