Transfinite Recursion

Abstract

The process of “definition by induction” has a transfinite analogue. The ordinary recursion theorem constructs a function on ω; the raw material is a way of getting the value of the function at each non-zero element n of ω from its value at the element preceding n. The transfinite analogue constructs a function on any well ordered set W; the raw material is a way of getting the value of the function at each element a of W from its values at all the predecessors of a.