Die Widerspruchsfreiheit der reinen Zahlentheorie

@article{Gentzen1936DieWD,
  title={Die Widerspruchsfreiheit der reinen Zahlentheorie},
  author={G. Gentzen},
  journal={Mathematische Annalen},
  year={1936},
  volume={112},
  pages={493-565}
}
  • G. Gentzen
  • Published 1936
  • Mathematics
  • Mathematische Annalen
View on Springer
493 Citations
Highly Influential Citations
32
Background Citations
115
Methods Citations
52
Results Citations
2

493 Citations

Citation Type

Citation Type

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We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as… Expand
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.… Expand
L O ] 1 8 M ay 2 01 4 Goodstein ’ s theorem revisited
  • 2014
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… Expand
Size-based termination of higher-order rewriting
  • F. Blanqui
  • Computer Science, Mathematics
  • Journal of Functional Programming
  • 2018
TLDR
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. Expand
Essay Review
Theories of truth and the maxim of minimal mutilation
Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up… Expand
A Semantic Framework for Proof Evidence
TLDR
The foundational proof certificates (FPC) framework is proposed, which allows both producers of proof certificates and the checkers of those certificates to have a clear formal definition of the semantics of a wide variety of proof evidence. Expand
Ancestral Logic: A Proof Theoretical Study
TLDR
A Gentzen-style proof system TC G is developed which is sound for ancestral logic, and its equivalence to previous systems for the reflexive transitive closure operator is proved by providing translation algorithms between them. Expand
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References

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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… Expand
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… Expand
Formale Beweise und die Entscheidbarkeit
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Über das Unendliche
Begründung des „tertium non datur” mittels der Hilbertschen Theorie der Widerspruchsfreiheit
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,… Expand