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On the intuitionistic strength of monotone inductive definitions

  • Sergei Tupailo (a1)
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.

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[Fef75]Feferman, S., A language and axioms for explicit mathematics, Algebra and logic, Lecture Notes in Mathematics, vol. 450, Springer, 1975, pp. 87139.
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[Tu03]Tupailo, S., 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. 165196.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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