Well quasi-orders and the functional interpretation

The purpose of this article is to study the role of Godel’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.

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