FUNCTIONAL INTERPRETATIONS

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The book explores functional interpretations of arithmetic, analysis, and set theory, tracing back to Gödel's Dialectica interpretation. It examines how higher type operations can simplify consistency issues in arithmetic by addressing computability of primitive recursive functionals. Key interpretations, including the Dialectica and Diller-Nahm interpretations, are analyzed within Heyting and Peano arithmetic, extending to constructive and classical analysis and set theory. The text also discusses Kreisel's and Troelstra's contributions, offering insights into relative consistency and axiomatic characterizations of functional translations.