Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics)

This is the first treatment in book format of proof-theoretic transformations – known as proof interpretations – that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as – via extended case studies – carrying out some of these applications in full detail. This subject has historical roots in the 1950s. This book for the first time tells the whole story.

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