A computational interpretation of Zorn's lemma
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We give a computational interpretation to an abstract instance of Zorn's lemma formulated as a wellfoundedness principle in the language of arithmetic in all finite types. This is achieved through Gödel's functional interpretation, and requires the introduction of a novel form of recursion over chain complete partial orders whose existence in the model of total continuous functionals is proven using domain theoretic techniques. We show that a realizer for the functional interpretation of open induction over the lexicographic ordering on sequences follows as a simple application of our main results.
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