標題: Titlebook: Gentzen‘s Centenary; The Quest for Consis Reinhard Kahle,Michael Rathjen Book 2015 Springer International Publishing Switzerland 2015 Consi [打印本頁] 作者: fathom 時間: 2025-3-21 16:09
書目名稱Gentzen‘s Centenary影響因子(影響力)
書目名稱Gentzen‘s Centenary影響因子(影響力)學科排名
書目名稱Gentzen‘s Centenary網(wǎng)絡(luò)公開度
書目名稱Gentzen‘s Centenary網(wǎng)絡(luò)公開度學科排名
書目名稱Gentzen‘s Centenary被引頻次
書目名稱Gentzen‘s Centenary被引頻次學科排名
書目名稱Gentzen‘s Centenary年度引用
書目名稱Gentzen‘s Centenary年度引用學科排名
書目名稱Gentzen‘s Centenary讀者反饋
書目名稱Gentzen‘s Centenary讀者反饋學科排名
作者: Judicious 時間: 2025-3-21 20:55
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.作者: 向下 時間: 2025-3-22 02:17 作者: Mediocre 時間: 2025-3-22 05:11 作者: gene-therapy 時間: 2025-3-22 11:46 作者: 比賽用背帶 時間: 2025-3-22 16:42
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.作者: 比賽用背帶 時間: 2025-3-22 17:39
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.作者: crumble 時間: 2025-3-23 01:06 作者: 陳列 時間: 2025-3-23 03:27 作者: 痛打 時間: 2025-3-23 05:39 作者: 氣候 時間: 2025-3-23 10:50 作者: 原告 時間: 2025-3-23 14:42
Book 2015e-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. ??.作者: 傾聽 時間: 2025-3-23 20:03
https://doi.org/10.1007/978-3-642-93604-3t. In a letter to Bernays dated November 4, 1935, Gentzen protested this evaluation; but then, in another letter to him dated December 11, 1935, he admits that the ‘critical inference in my consistency proof is defective’.作者: 一瞥 時間: 2025-3-24 00:32 作者: 誓言 時間: 2025-3-24 04:33 作者: Altitude 時間: 2025-3-24 08:01 作者: Stable-Angina 時間: 2025-3-24 12:52 作者: 流浪 時間: 2025-3-24 18:34 作者: reptile 時間: 2025-3-24 21:25 作者: 緯度 時間: 2025-3-25 02:57
https://doi.org/10.1007/978-3-642-91399-0In this article we study subsystems .. of the theory .. in which fixed point induction is restricted to properly stratified formulas.作者: 事物的方面 時間: 2025-3-25 04:54
Gentzen’s Consistency Proof in ContextGentzen’s celebrated consistency proof—or proofs, to distinguish the different variations he gave.—of Peano Arithmetic in terms of transfinite induction up to the ordinal. . can be considered as the birth of modern proof theory.作者: Hemiparesis 時間: 2025-3-25 07:55
Gentzen’s Anti-Formalist ViewsIn June of 1936 Gentzen gave a lecture at Heinrich Scholz’ seminar in Münster. The title of the lecture was “Der Unendlichkeitsbegriff in der Mathematik.”.作者: BOLUS 時間: 2025-3-25 14:32
On Gentzen’s First Consistency Proof for ArithmeticIf nowadays “Gentzen’s consistency proof for arithmetic” is mentioned, one usually refers to [3] while Gentzen’s first (published) consistency proof, i.e.?[2], is widely unknown or ignored. The present paper is intended to change this unsatisfactory situation by presenting [2, IV.?Abschnitt] in a slightly modified and modernized form.作者: 諄諄教誨 時間: 2025-3-25 18:33
A Direct Gentzen-Style Consistency Proof for Heyting ArithmeticGerhard Gentzen was the first to give a proof of the consistency of Peano Arithmetic and in all he worked out four different proofs between 1934 and 1939. The second proof was published as [1], the third as [2], and the fourth as [3]. The first proof was published posthumously in English translation in [4] and in the German original as?[5].作者: Deject 時間: 2025-3-25 21:43
Proof Theory for Theories of Ordinals III: , -ReflectionThis paper deals with a proof theory for a theory T. of .-reflecting ordinals using a system . of ordinal diagrams. This is a sequel to the previous one (Arai, Ann Pure Appl Log 129:39–92, 2004) in which a theory for .-reflecting ordinals is analysed proof-theoretically.作者: 行為 時間: 2025-3-26 01:32 作者: abysmal 時間: 2025-3-26 05:25 作者: 向外供接觸 時間: 2025-3-26 09:23
https://doi.org/10.1007/978-3-662-29053-8ication of how to reach any ordinal .. In his analysis Gentzen used ordinals in Cantor normal form. We shall look at ordinals as given by finite trees and then see how the climbing up to . can be justified there with methods from first order arithmetic, and methods to use where we climb above it.作者: 里程碑 時間: 2025-3-26 12:45 作者: CURT 時間: 2025-3-26 17:26
Climbing Mount ,ication of how to reach any ordinal .. In his analysis Gentzen used ordinals in Cantor normal form. We shall look at ordinals as given by finite trees and then see how the climbing up to . can be justified there with methods from first order arithmetic, and methods to use where we climb above it.作者: 褲子 時間: 2025-3-26 23:06
https://doi.org/10.1007/978-3-319-10103-3Consistency Proof; Gentzen Formal Systems; Gentzen‘s Main Theorem; Ordinal Analysis; Proof Theory作者: 窗簾等 時間: 2025-3-27 01:59 作者: Adherent 時間: 2025-3-27 09:05 作者: 微枝末節(jié) 時間: 2025-3-27 13:00
https://doi.org/10.1007/978-3-642-50901-8e most metamathematical investigations are focused on carrying out mathematical reductions, we claim that in order to give a full substitute for Hilbert’s program, one should not stop with purely mathematical investigations, but give an answer to the question why one should believe that all theorems作者: 變異 時間: 2025-3-27 15:15
https://doi.org/10.1007/978-3-642-91605-2 that the consistency proof was based on an explicit semantic notion of correctness as . of sequents and a proof that steps of derivation maintain reducibility. A crucial point in the latter was Gentzen’s . that stated, in analogy to his famous ., that composition of sequents maintains reducibility.作者: Acupressure 時間: 2025-3-27 21:09
Verbindung von Tr?gern mit S?ulen method used in Gentzen’s second consistency proof. Gentzen explained the intuitive idea behind his proof by informally arguing for the possibility of a normalization theorem of natural deduction, but what he actually proved was a special case of the Hauptsatz for a sequent calculus formalization of作者: guzzle 時間: 2025-3-28 00:03 作者: HAIL 時間: 2025-3-28 05:06
https://doi.org/10.1007/978-3-322-98670-2own as Goodstein sequences. This chapter revisits Goodstein’s 1944 paper. In light of new historical details found in a correspondence between Bernays and Goodstein, we address the question of how close Goodstein came to proving an independence result for .. We also present an elementary proof of th作者: 袖章 時間: 2025-3-28 06:40 作者: CRUC 時間: 2025-3-28 14:29 作者: 最小 時間: 2025-3-28 18:19
https://doi.org/10.1007/978-3-662-29053-8ication of how to reach any ordinal .. In his analysis Gentzen used ordinals in Cantor normal form. We shall look at ordinals as given by finite trees and then see how the climbing up to . can be justified there with methods from first order arithmetic, and methods to use where we climb above it.作者: Accord 時間: 2025-3-28 22:42 作者: ANTIC 時間: 2025-3-28 23:36
The Use of Trustworthy Principles in a Revised Hilbert’s Programe most metamathematical investigations are focused on carrying out mathematical reductions, we claim that in order to give a full substitute for Hilbert’s program, one should not stop with purely mathematical investigations, but give an answer to the question why one should believe that all theorems作者: 耐寒 時間: 2025-3-29 06:44 作者: 可卡 時間: 2025-3-29 07:14
A Note on How to Extend Gentzen’s Second Consistency Proof to a Proof of Normalization for First Ord method used in Gentzen’s second consistency proof. Gentzen explained the intuitive idea behind his proof by informally arguing for the possibility of a normalization theorem of natural deduction, but what he actually proved was a special case of the Hauptsatz for a sequent calculus formalization of作者: nettle 時間: 2025-3-29 14:47 作者: 審問 時間: 2025-3-29 18:49
Goodstein’s Theorem Revisitedown as Goodstein sequences. This chapter revisits Goodstein’s 1944 paper. In light of new historical details found in a correspondence between Bernays and Goodstein, we address the question of how close Goodstein came to proving an independence result for .. We also present an elementary proof of th作者: Hyperplasia 時間: 2025-3-29 22:48
Cut Elimination In Situ the proof. For propositional logic, this requires converting a proof from tree-like to dag-like form, but at most doubles the number of lines in the proof. For first-order logic, the proof size can grow exponentially, but the proof has a succinct description and is polynomial time uniform. We use d作者: Implicit 時間: 2025-3-29 23:54
Spector’s Proof of the Consistency of Analysisme dedicated to Gerhard Gentzen, known for his epoch-making consistency proof of Peano arithmetic ., Spector’s proof of consistency of analysis is discussed. Gentzen’s approach to consistency proofs has been systematically developed and generalized by the German school of proof theory (Schütte, Pohl作者: 從容 時間: 2025-3-30 04:20 作者: barium-study 時間: 2025-3-30 08:29
Semi-Formal Calculi and Their Applicationses was already suggested by David Hilbert in his paper “Die Grundlegung der elementaren Zahlentheorie” [6] and was later systematically used by Kurt Schütte in his work on proof theory. The heigths of proof trees in a semi-formal system are canonically measured by ordinals. Therefore, in contrast to作者: florid 時間: 2025-3-30 13:11
https://doi.org/10.1007/978-3-642-50901-8tamathematical investigations. We investigate three approaches for trustworthy principles, namely ordinal notation systems built from below, Martin-L?f type theory, and Feferman’s system of explicit mathematics. We will review what is known about the strength up to which direct validation can be pro作者: 解脫 時間: 2025-3-30 17:54
https://doi.org/10.1007/978-3-322-98670-2the same vein we also wonder whether the search for strictly mathematical examples of an incompleteness in . really attained its “holy grail” status before the late 1970s. Almost no direct moral is ever given; rather, the paper strives to lay out evidence for the reader to consider and have the read
