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

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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.

Accord

ANTIC

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

耐寒

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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

nettle

审问

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

Hyperplasia

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

Implicit

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

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