2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219902Extending Gödel's \emph{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.minor corrections and changesLogic03F25; 03F10; 03D70text