## Paper: A Computational Interpretation of Open Induction (at LICS 2004)

**Ulrich Berger**

### Abstract

We study the proof-theoretic and computational properties of open induction, a principle which is classically equivalent to Nash-Williams' minimal-bad-sequence argument and also to (countable) dependent choice (and hence contains full classical analysis). We show that, intuitionistically, open induction and dependent choice are quite different: Unlike dependent choice, open induction is closed under negative- and -translation, and therefore proves the same II_2^0-formulas (over not necessarily decidable, basic predicates) with classical or intuitionistic arithmetic. Via modified realizability we obtain a new direct method for extracting programs from classical proofs of II_2^0-formulas using open induction. We also show that the computational interpretation of classical countable choice given by Berardi, Bezen and Coquand [On the computational content of the axiom of choice] can be derived from our results.

### BibTeX

@InProceedings{Berger-AComputationalInter, author = {Ulrich Berger}, title = {A Computational Interpretation of Open Induction}, booktitle = {Proceedings of the Nineteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2004)}, year = {2004}, month = {July}, pages = {326--334}, location = {Turku, Finland}, publisher = {IEEE Computer Society Press} }