Realization of Analysis into Explicit Mathematics

Journal of Symbolic Logic 66 (4):1848-1864 (2001)
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Abstract

We define a novel interpretation $\mathscr{R}$ of second order arithmetic into Explicit Mathematics. As a difference from standard $\mathscr{D}$-interpretation, which was used before and was shown to interpret only subsystems proof-theoretically weaker than $T_0$, our interpretation can reach the full strength of $T_0$. The $\mathscr{R}$-interpretation is an adaptation of Kleene's recursive realizability, and is applicable only to intuitionistic theories.

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