Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of...

Gentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen in 1936. It shows that the Peano axioms of...

every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology...

(or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in his...

it is typically read as "for all". It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's turned E notation for existential...

if it is classically satisfiable. The Gödel–Gentzen translation (named after Kurt Gödel and Gerhard Gentzen) associates with each formula φ in a first-order...

include a second order completeness axiom. In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new light on the problem. Some feel that Gödel's...

prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified...

modern form was independently proposed by the German mathematician Gerhard Gentzen in 1933, in a dissertation delivered to the faculty of mathematical...

and SS officer executed for war crimes Gerhard Gentzen (1909–1945), German mathematician and logician Gerhard Armauer Hansen (1841–1912), Norwegian physician...

founders of natural deduction, which he discovered independently of Gerhard Gentzen in the 1930s. He is also known for his research into paraconsistent...

result was proven and extended to intuitionistic predicate logic by Gerhard Gentzen (1934, 1935). Stephen Cole Kleene (1945) proved that Heyting arithmetic...

Gebhardt Arnold Gehlen Willi Geiger (judge) Hans-Dietrich Genscher Gerhard Gentzen Karl Genzken Achim Gercke Herbert Gerigk Karl Gerland Kurt Gerstein...

indicate universal quantification. It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's ∃ {\displaystyle \exists...

inference. The first systems of natural deduction were developed by Gerhard Gentzen and Stanislaw Jaskowski in the 1930s. The core motivation was to give...

meaning of propositions with the roles that they can play in inferences. Gerhard Gentzen, Dag Prawitz and Michael Dummett are generally seen as the founders...

deduction, truth trees and truth tables. Natural deduction was invented by Gerhard Gentzen and Stanisław Jaśkowski. Truth trees were invented by Evert Willem...

2009, p. 128. Eckart Menzler-Trott, Logic's Lost Genius: The Life of Gerhard Gentzen. American Mathematical Society, 2007, p. 200. Deichmann, p. 281. Erhard...

in a theory that T itself can prove to be consistent. For example, Gerhard Gentzen proved the consistency of Peano arithmetic in a different system that...

partisans. 1945 – Dietrich Bonhoeffer was executed by hanging. 1945 – Gerhard Gentzen was detained in a prison camp by the Russian forces, where he died...

numbers set) 1930 Edmund Landau ∀ universal quantifier (for all) 1935 Gerhard Gentzen → arrow (for function notation) 1936 (to denote images of specific...

Jaśkowski (1929) and Gerhard Gentzen (1934) independently provided such systems, called calculi of natural deduction, with Gentzen's approach introducing...

2023. Menzler-Trott, Eckart (2008). Logic's Lost Genius: The Life of Gerhard Gentzen. AMS. p. 115. ISBN 978-0-8218-3550-0. Akademisk Boldklub. "AB's historie"...

In 1936, Gerhard Gentzen gave a proof of the consistency of Peano's axioms, using transfinite induction up to an ordinal called ε0. Gentzen explained:...

Translated as 'The consistency of arithmetic', in The collected papers of Gerhard Gentzen, M. E. Szabo (ed.), 1969. D. Hilbert. 'Die Grundlegung der elementaren...

)\to ((\phi \to \chi )\land (\chi \to \phi ))} using conjunction. Gerhard Gentzen discovered that a simple restriction of his system LK (his sequent...

rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934." According to Willard Van Orman Quine...

ISBN 9780271026954. Trott, Eckart (2007). Logic's lost genius : the life of Gerhard Gentzen. Providence, RI London: American Mathematical Society London Mathematical...

logic Relevant logic Proof-theoretic semantics Ludics System F Gerhard Gentzen Gentzen's consistency proof Reverse mathematics Nonfirstorderizability Interpretability...

extraordinary professor without tenure. His most successful student there was Gerhard Gentzen. After Nazi Germany enacted the Law for the Restoration of the Professional...