Realization of analysis into explicit mathematics

Journal of Symbolic Logic 66 (4):1848-1864 (2001)
We define a novel interpretation R of second order arithmetic into Explicit Mathematics. As a difference from standard 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 R-interpretation is an adaptation of Kleene's recursive realizability, and is applicable only to intuitionistic theories
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DOI 10.2307/2694980
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The Strength of Some Martin-Löf Type Theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Well-Ordering Proofs for Martin-Löf Type Theory.Anton Setzer - 1998 - Annals of Pure and Applied Logic 92 (2):113-159.

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