Download PDFOpen PDF in browserA Direct Computational Interpretation of Second-Order Arithmetic via Update RecursionEasyChair Preprint 876811 pages•Date: August 31, 2022AbstractSecond-order arithmetic has two kinds of computational interpretations: via Spector's bar recursion of via Girard's polymorphic lambda-calculus. Bar recursion interprets the negative translation of the axiom of choice which, combined with an interpretation of the negative translation of the excluded middle, gives a computational interpretation of the negative translation of the axiom scheme of specification. It is then possible to instantiate universally quantified sets with arbitrary formulas (second-order elimination). On the other hand, polymorphic lambda-calculus interprets directly second-order elimination by means of polymorphic types. The present work aims at bridging the gap between these two interpretations by interpreting directly second-order elimination through update recursion, which is a variant of bar recursion. Keyphrases: bar recursion, polymorphism, realizability, second-order arithmetic
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