事物的方面
发表于 2025-3-25 04:54:52
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.
Hemiparesis
发表于 2025-3-25 07:55:22
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.”.
BOLUS
发表于 2025-3-25 14:32:26
On Gentzen’s First Consistency Proof for ArithmeticIf nowadays “Gentzen’s consistency proof for arithmetic” is mentioned, one usually refers to while Gentzen’s first (published) consistency proof, i.e. , is widely unknown or ignored. The present paper is intended to change this unsatisfactory situation by presenting in a slightly modified and modernized form.
谆谆教诲
发表于 2025-3-25 18:33:14
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 , the third as , and the fourth as . The first proof was published posthumously in English translation in and in the German original as .
Deject
发表于 2025-3-25 21:43:48
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.
行为
发表于 2025-3-26 01:32:49
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abysmal
发表于 2025-3-26 05:25:56
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向外供接触
发表于 2025-3-26 09:23:12
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.
里程碑
发表于 2025-3-26 12:45:49
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CURT
发表于 2025-3-26 17:26:53
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.