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September 2004 On the intuitionistic strength of monotone inductive definitions
Sergei Tupailo
J. Symbolic Logic 69(3): 790-798 (September 2004). DOI: 10.2178/jsl/1096901767

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.

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Sergei Tupailo. "On the intuitionistic strength of monotone inductive definitions." J. Symbolic Logic 69 (3) 790 - 798, September 2004. https://doi.org/10.2178/jsl/1096901767

Information

Published: September 2004
First available in Project Euclid: 4 October 2004

zbMATH: 1070.03040
MathSciNet: MR2078922
Digital Object Identifier: 10.2178/jsl/1096901767

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 3 • September 2004
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