Journal of Symbolic Logic

On the intuitionistic strength of monotone inductive definitions

Sergei Tupailo

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We prove here that the intuitionistic theory T0↾+UMIDN, or even EETJ↾+UMIDN, of Explicit Mathematics has the strength of Π21-CA0. In Section 1 we give a double-negation translation for the classical second-order μ-calculus, which was shown in [Moe02] to have the strength of Π21-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.

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J. Symbolic Logic, Volume 69, Issue 3 (2004), 790-798.

First available in Project Euclid: 4 October 2004

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Tupailo, Sergei. On the intuitionistic strength of monotone inductive definitions. J. Symbolic Logic 69 (2004), no. 3, 790--798. doi:10.2178/jsl/1096901767.

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