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Monotone inductive definitions in explicit mathematics

Published online by Cambridge University Press:  12 March 2014

Michael Rathjen
Michael Rathjen*
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305, E-mail: rathjen@math.stanford.edu
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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.

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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 1 , March 1996 , pp. 125 - 146
Copyright
Copyright © Association for Symbolic Logic 1996

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References

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