Journal of Symbolic Logic

On the intuitionistic strength of monotone inductive definitions

Sergei Tupailo

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 4 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1096901767

Digital Object Identifier
doi:10.2178/jsl/1096901767

Mathematical Reviews number (MathSciNet)
MR2078922

Zentralblatt MATH identifier
1070.03040

Citation

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


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References

  • S. Feferman A language and axioms for explicit mathematics, Algebra and logic, Lecture Notes in Mathematics, vol. 450, Springer,1975, pp. 87--139.
  • T. Glaß, M. Rathjen, and A. Schlüter On the proof-theoretic strength of monotone induction in explicit mathematics, Annals of Pure and Applied Logic, vol. 85 (1997), pp. 1--46.
  • M. Möllerfeld Generalized Inductive Definitions. The $\mu$-calculus and \POT-comprehension, Ph.D. thesis, Universität Münster,2002.
  • M. Rathjen Monotone inductive definitions in explicit mathematics, Journal of Symbolic Logic, vol. 61 (1996), pp. 125--146.
  • S. Takahashi Monotone inductive definitions in a constructive theory of functions and classes, Annals of Pure and Applied Logic, vol. 42 (1989), pp. 255--297.
  • S. Tupailo Realization of constructive set theory into Explicit Mathematics: a lower bound for impredicative Mahlo universe, Annals of Pure and Applied Logic, vol. 120 (2003), no. 1-3, pp. 165--196.