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On this page you'll find 10+ example sentences with Gentzen. Discover how to use the word correctly in a sentence.

Rare word

Gentzen in a sentence

Using Gentzen

  • In the example corpus, gentzen often appears in combinations such as: gentzen was.

Context around Gentzen

  • Average sentence length in these examples: 25.9 words
  • Position in the sentence: 5 start, 4 middle, 1 end
  • Sentence types: 10 statements, 0 questions, 0 exclamations

Often before:

deduction 1×

Often after:

joined 1× published 1× negative 1×

Sentence patterns with Gentzen

These short patterns come directly from the example sentences and show how the word is often embedded:

form of gentzen s consistency 1× gentzen joined the 1× gentzen published his 1× method and gentzen s consistency 1× much of gentzen s work 1× natural deduction gentzen was motivated 1× or not gentzen s proof 1× since gentzen s work 1×

Sentence openings and endings

Common sentence openings:

bernays included a 1× gentzen joined the 1× gentzen published his 1× in a series 1× results such as 1× since gentzen s 1×

Common sentence endings:

a precise definition 1× and computer science 1× arithmetic in 1936 1× judgments and connectives 1× natural deduction framework 1× of number theory 1×

Words around Gentzen

Just before it in the word index:

gentse 6 gents 40 gentry 187 gentrust 2 gentrup 2 gentronix 2

Just after it in the word index:

gentzkow 2 gentzler 3 genu 2 genuflect 4 genuflecting 4 genuflection 4

Similar in corpus frequency:

aab 14 aamer 14 aave 14 abadan 14 abdelmadjid 14 abdulkarim 14

Corpus analysis for Gentzen

  • In this selection, "gentzen" usually appears near the start of the sentence. The average example has 25.9 words, and this corpus slice is mostly made up of statements.
  • Around the word, deduction, joined, published and negative stand out and add context to how "gentzen" is used.
  • Recognizable usage signals include form of gentzen s consistency and gentzen joined the. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "gentzen" sits close to words such as aab, aamer and aave, which helps place it inside the broader word index.

Example types with gentzen

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Gentzen published his consistency proof for first-order arithmetic in 1936. (11 words)

The second volume in 1939 included a form of Gentzen's consistency proof for arithmetic. (15 words)

Gentzen joined the Sturmabteilung in November 1933 although he was by no means compelled to do so. (17 words)

Longer example sentences

Bernays included a full proof of the incompleteness theorems in the second volume of Grundlagen der Mathematik (1939), along with additional results of Ackermann on the ε-substitution method and Gentzen's consistency proof of arithmetic. (36 words)

Whether or not Gentzen's proof meets the requirements Hilbert envisioned is unclear: there is no generally accepted definition of exactly what is meant by a finitistic proof, and Hilbert himself never gave a precise definition. (36 words)

Results such as the Gödel–Gentzen negative translation show that it is possible to embed (or translate) classical logic into intuitionistic logic, allowing some properties about intuitionistic proofs to be transferred back to classical proofs. (35 words)

Example sentences (10)

Bernays included a full proof of the incompleteness theorems in the second volume of Grundlagen der Mathematik (1939), along with additional results of Ackermann on the ε-substitution method and Gentzen's consistency proof of arithmetic.

Gentzen joined the Sturmabteilung in November 1933 although he was by no means compelled to do so.

Gentzen published his consistency proof for first-order arithmetic in 1936.

In a series of seminars in 1961 and 1962 Prawitz gave a comprehensive summary of natural deduction calculi, and transported much of Gentzen's work with sequent calculi into the natural deduction framework.

Results such as the Gödel–Gentzen negative translation show that it is possible to embed (or translate) classical logic into intuitionistic logic, allowing some properties about intuitionistic proofs to be transferred back to classical proofs.

Since Gentzen's work, natural deduction and sequent calculi have been widely applied in the fields of proof theory, mathematical logic and computer science.

The second volume in 1939 included a form of Gentzen's consistency proof for arithmetic.

The system presented in this article is a minor variation of Gentzen's or Prawitz's formulation, but with a closer adherence to Martin-Löf 's description of logical judgments and connectives.

Thus arose a "calculus of natural deduction".) Gentzen was motivated by a desire to establish the consistency of number theory.

Whether or not Gentzen's proof meets the requirements Hilbert envisioned is unclear: there is no generally accepted definition of exactly what is meant by a finitistic proof, and Hilbert himself never gave a precise definition.

Common combinations with gentzen

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "gentzen" in a sentence?
An example: "Bernays included a full proof of the incompleteness theorems in the second volume of Grundlagen der Mathematik (1939), along with additional results of Ackermann on the ε-substitution method and Gentzen's consistency proof of arithmetic." This page contains 10+ example sentences with the word "gentzen" from authentic English texts.
How many example sentences with "gentzen" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "gentzen", drawn from a database of millions of English sentences.