Journal of Symbolic Logic

Monotone Inductive Definitions in Explicit Mathematics

Michael Rathjen

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.


The context for this paper is Feferman's theory of explicit mathematics, $\mathbf{T_0}$. We address a problem that was posed in [6]. Let $\mathbf{MID}$ 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 $\mathbf{T_0} + \mathbf{MID}$, 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 $\mathbf{MID}$, when adjoined to classical $\mathbf{T_0}$, leads to a much stronger theory than $\mathbf{T_0}$.

Article information

J. Symbolic Logic, Volume 61, Issue 1 (1996), 125-146.

First available in Project Euclid: 6 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Rathjen, Michael. Monotone Inductive Definitions in Explicit Mathematics. J. Symbolic Logic 61 (1996), no. 1, 125--146.

Export citation