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Recursion on the countable functionals

New York: Springer Verlag (1980)

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  1. Reduction of higher type levels by means of an ordinal analysis of finite terms.Jan Terlouw - 1985 - Annals of Pure and Applied Logic 28 (1):73-102.
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  • A constructive manifestation of the Kleene–Kreisel continuous functionals.Martín Escardó & Chuangjie Xu - 2016 - Annals of Pure and Applied Logic 167 (9):770-793.
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  • The computational content of Nonstandard Analysis.Sam Sanders - unknown
    Kohlenbach's proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel's pioneering work on the so-called unwinding of proofs. The proof mining of classical mathematics is rather restricted in scope due to the existence of sentences without computational content which are provable from the law of excluded middle and which involve only two quantifier alternations. By contrast, we show that the proof mining of classical Nonstandard Analysis has a very (...)
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