Monotone inductive definitions in explicit mathematics
Michael Rathjen · Journal of Symbolic Logic · 1996
Abstract The context for this paper is Feferman's theory of explicit mathematics, T0. We address a problem that was posed in [6]. Let MID be the principle stating that any monotone operation on classifications has a least fixed point. The main objective of this paper is to show that T0 + MID, when based on classical logic, also proves the existence of non-monotone inductive definitions that arise from arbitrary extensional operations on classifications. From the latter we deduce that MID, when adjoined to classical T0, leads to a much stronger theory than T0.