Gerhard Gentzen has been described as logics lost genius, whom G?del called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzens enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzens original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.
The book collects for the first time individual studies which focus solely on this aspect of Gentzens work. Because they admirably elucidate the historical, philosophical, and technical facets of his foundational papers in ordinal proof theory, the book can be recommended to everyone interested in these topics. (David Binder, Journal for General Philosophy of Science, Vol. 49, 2018)
The volume is undoubtedly of a high-level technical content and thus of great interest for computer scientists and mathematical logicians. However, thanks to the numerous chapters containing philosophical reflections and historical information, the volume is also appealing for philosophers of logic. (Francesca Poggiolesi, History and Philosophy of Logic, Vol. 38 (3), March, 2017)
The articles in this collection clearly offer a wide and lively description of Gentzens work and of Gentzens legacy. & This volume will be for years to come an important key tool not only for people working in reductive and ordinal proof theory, but also for anyone more in general interested in the field of proof theory. (Enrico Moriconi, History and Philosophy of Logic,ló€
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