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Functional interpretation and inductive definitions

Published:2009-12 Issue:4 Volume:74 Page:1100-1120
ISSN:0022-4812
Container-title:The Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

Avigad Jeremy,Towsner Henry

Abstract

AbstractExtending 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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference36 articles.

1. Troelstra A. S. , Introductory note to 1958 and 1972, In Feferman et al. [16], pp. 217–241.

2. Iterated inductive definitions, trees and ordinals

3. Proof Theory: Some Applications of Cut-Elimination

4. Shoenfield is Gödel after Krivine

5. Classically and intuitionistically provably recursive functions

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