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