Predicative functionals and an interpretation of ⌢ID<ω

In 1958 Gödel published his Dialectica interpretation, which reduces classical arithmetic to a quantifier-free theory T axiomatizing the primitive recursive functionals of finite type
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DOI 10.1016/S0168-0072(97)00045-6
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Justus Diller (2002). Logical Problems of Functional Interpretations. Annals of Pure and Applied Logic 114 (1-3):27-42.

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