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On the intuitionistic strength of monotone inductive definitions

Published online by Cambridge University Press:  12 March 2014

Sergei Tupailo*
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England, E-mail: s.tupailo@maths.leeds.ac.uk

Abstract.

We prove here that the intuitionistic theory T0↾ + UMIDN. or even EETJ↾ + UMIDN, of Explicit Mathematics has the strength of –CA0. In Section 1 we give a double-negation translation for the classical second-order μ-calculus, which was shown in [Mö02] to have the strength of –CA0. In Section 2 we interpret the intuitionistic μ-calculus in the theory EETJ↾ + UMIDN. The question about the strength of monotone inductive definitions in T0 was asked by S. Feferman in 1982, and — assuming classical logic — was addressed by M. Rathjen.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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