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Titlebook: Gentzen‘s Centenary; The Quest for Consis Reinhard Kahle,Michael Rathjen Book 2015 Springer International Publishing Switzerland 2015 Consi

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发表于 2025-3-21 16:09:26 | 显示全部楼层 |阅读模式
书目名称Gentzen‘s Centenary
副标题The Quest for Consis
编辑Reinhard Kahle,Michael Rathjen
视频video
概述Provides a comprehensive picture of proof-theoretic investigations following Gerhard Gentzen‘s seminal work.Revisits and re-evaluates Gentzen‘s original proof(s) of the consistency of arithmetic.Inclu
图书封面Titlebook: Gentzen‘s Centenary; The Quest for Consis Reinhard Kahle,Michael Rathjen Book 2015 Springer International Publishing Switzerland 2015 Consi
描述.Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s 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.   .
出版日期Book 2015
关键词Consistency Proof; Gentzen Formal Systems; Gentzen‘s Main Theorem; Ordinal Analysis; Proof Theory
版次1
doihttps://doi.org/10.1007/978-3-319-10103-3
isbn_softcover978-3-319-10102-6
isbn_ebook978-3-319-10103-3
copyrightSpringer International Publishing Switzerland 2015
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https://doi.org/10.1007/978-3-642-91605-2 first proof evolved into one based on transfinite induction. Traces of the . that was founded on intuitionistic ideas disappeared, and Gentzen developed instead transfinite induction further into a general ordinal proof theory.
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Neuere Methoden der Lichterzeugung,irect, global constructions that give polynomial time methods for removing all top-level cuts from proofs. By exploiting prenex representations, this extends to removing all cuts, with final proof size near-optimally bounded superexponentially in the alternation of quantifiers in cut formulas.
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Cut Elimination In Situirect, global constructions that give polynomial time methods for removing all top-level cuts from proofs. By exploiting prenex representations, this extends to removing all cuts, with final proof size near-optimally bounded superexponentially in the alternation of quantifiers in cut formulas.
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