Functional Interpretation and Inductive Definitions

Abstract
Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees
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Ulrich Kohlenbach (1999). On the No-Counterexample Interpretation. Journal of Symbolic Logic 64 (4):1491-1511.
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