# Die Widerspruchsfreiheit der reinen Zahlentheorie

@article{Gentzen1936DieWD,
title={Die Widerspruchsfreiheit der reinen Zahlentheorie},
author={Gerhard Gentzen},
journal={Mathematische Annalen},
year={1936},
volume={112},
pages={493-565}
}
• G. Gentzen
• Published 1 December 1936
• Mathematics
• Mathematische Annalen
505 Citations
On the Intuitionistic Background of Gentzen's 1935 and 1936 Consistency Proofs and Their Philosophical Aspects
Gentzen’s three consistency proofs for elementary number theory have a common aim that originates from Hilbert’s Program, namely, the aim to justify the application of classical reasoning to
Decoding Gentzen's Notation
In this note we consider Gentzen's first ordinal notation, used in his first published proof of the consistency of Peano Arithmetic (1936). It is a decimal notation, quite different from our current
Commentary and Illocutionary Expressions in Linear Calculi of Natural Deduction
• Computer Science
• 2017
A linear natural deduction calculus is presented that makes use of formal illocutionsary expressions in such a way that unique readability for derivations is guaranteed – thus showing that formalizing illocutionary expressions can eliminate the need for commentary.
Goodstein’s Theorem Revisited
Prompted by Gentzen’s 1936 consistency proof, Goodstein found a close fit between descending sequences of ordinals $$<\varepsilon _{0}$$ and sequences of integers, now known as Goodstein sequences.
L O ] 1 8 M ay 2 01 4 Goodstein ’ s theorem revisited
Inspired by Gentzen’s 1936 consistency proof, Goodstein found a close fit between descending sequences of ordinals < ε0 and sequences of integers, now known as Goodstein sequences. This article
Proof Theory : From arithmetic to set theory
In his Inaugural Dissertation from 1935 (published as [41]), Gentzen introduced his sequent calculus and employed the technique of cut elimination. As this is a tool of utmost importance in proof
A MATHEMATICAL COMMITMENT WITHOUT COMPUTATIONAL STRENGTH
• Anton Freund
• Computer Science
The Review of Symbolic Logic
• 2021
This work considers a proper extension of Peano arithmetic by a mathematically meaningful axiom scheme that consists of sentences that assert that each computably enumerable property of finite binary trees has a finite basis.
Systems of Logic Based on Ordinals
• A. Turing
• Computer Science
Alan Turing's Systems of Logic
• 2021
Representation and Reality by Language: How to Make a Home Quantum Computer?
A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored and the equivalence of that model to a quantum computer is demonstrated.
Size-based termination of higher-order rewriting
• F. Blanqui
• Computer Science
Journal of Functional Programming
• 2018
A general and modular criterion for the termination of simply typed λ-calculus extended with function symbols defined by user-defined rewrite rules is provided.

## References

SHOWING 1-7 OF 7 REFERENCES
Formale Beweise und die Entscheidbarkeit
----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung
Über die neue Grundlagenkrise der Mathematik
DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen,
Zum Hilbertschen Aufbau der reellen Zahlen
Um den Beweis fiir die yon Cantor aufgestellte Vermutung zu e~bringen, dal~ sich die Menge der ree|len Zahlen, d. h. der zaMentheoretischen I~unktionen, mi~ Hilfe der Zahlen de~ zweiten Zahlklasse
Die Vollständigkeit der Axiome des logischen Funktionenkalküls
Jakina da Whiteheadek eta Russellek logika eta matematika eraiki dutela ageriko zenbait proposizio axiomatzat hartuz, eta horietatik, zehatz azaldutako inferentzia printzipioetan oinarrituz, logikako