Monotone Inductive Definitions in Explicit Mathematics

The context for this paper is Feferman's theory of explicit mathematics, T 0. We address a problem that was posed in F 82]. Let MID be the principle stating that any monotone operation on classiications has a least xed point. The main objective of this paper is to show that T 0 + MID, when based on classical logic, also proves the existence of non-monotone inductive deenitions that arise from arbitrary extensional operations on classiications. From the latter we deduce that MID, when adjoined to classical T 0 , leads to a much stronger theory than T 0 .