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Well Quasi-orders and the Functional Interpretation

  • Thomas PowellEmail author
Chapter
Part of the Trends in Logic book series (TREN, volume 53)

Abstract

The purpose of this article is to study the role of Gödel’s functional interpretation in the extraction of programs from proofs in well quasi-order theory. The main focus is on the interpretation of Nash–Williams’ famous minimal bad sequence construction, and the exploration of a number of much broader problems which are related to this, particularly the question of the constructive meaning of Zorn’s lemma and the notion of recursion over the non-wellfounded lexicographic ordering on infinite sequences.

Notes

Acknowledgements

In developing the ideas of this article I have benefited greatly from numerous illuminating conversations with Ulrich Berger, Paulo Oliva and Monika Seisenberger. Moreover, I am grateful to the anonymous referee, whose extremely detailed review led to a much better version of the paper.

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Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

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