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Herbrand's Fundamental Theorem - an encyclopedia article

@article{Wirth2015HerbrandsFT,
  title={Herbrand's Fundamental Theorem - an encyclopedia article},
  author={Claus-Peter Wirth},
  journal={arXiv: Logic},
  year={2015}
}
Herbrand's Fundamental Theorem provides a constructive characterization of derivability in first-order predicate logic by means of sentential logic. Sometimes it is simply called "Herbrand's Theorem", but the longer name is preferable as there are other important "Herbrand theorems" and Herbrand himself called it "Th\'eor\`eme fondamental". It was ranked by Bernays [1957] as follows: "In its proof-theoretic form, Herbrand's Theorem can be seen as the central theorem of predicate logic. It… 
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References

SHOWING 1-10 OF 66 REFERENCES

Herbrand's Fundamental Theorem: The Historical Facts and their Streamlining

TLDR
The inner structure of Herbrand’s Fundamental Theorem and the questions of its quality and its depth are discussed and why Bernays called it “the central theorem of predicate logic” and considered the form of its expression to be “concise and felicitous”.

HERBRAND’s Fundamental Theorem in the Eyes of JEAN VAN HEIJENOORT

TLDR
The inner structure of Herbrand’s Fundamental Theorem and the questions of its quality and its depth are discussed and why Bernays called it “the central theorem of predicate logic” and considered the form of its expression to be “concise and felicitous”.

Historical Development of Modern Logic

Modern Logic began in 1879, the year in which Gottlob Frege (1848–1925) published his Begriffsschrift. In less than ninety pages this booklet presented a number of discoveries that changed the face

A note on the Entscheidungsproblem

  • A. Church
  • Mathematics
    Journal of Symbolic Logic
  • 1936
TLDR
It is shown that the general case of the Entscheidungsproblem is unsolvable in any system of symbolic logic which is adequate to a certain portion of arithmetic and is ω-consistent.

Principia Mathematica

THIS work contains some thousands of propositions, each, with its proof, expressed in a shorthand so concise that if they were all expanded into ordinary language, the room taken up would be ten

Symbolic Logic

MR. McCOLL still expresses surprise at my declining to answer a Yes or No question which he was pleased to put to me in NATURE (vol. xxiv. p. 124). It was, I should think, almost unique in a

Writing mathematics well

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Logic as calculus and logic as language

Answering Schroder’s criticisms of Begriffsschrift, Frege states that, unlike Boole’s, his logic is not a calculus ratiocinator, or not merely a calculus ratiocinator, but a lingua characterica.1 If

On computable numbers, with an application to the Entscheidungsproblem

  • A. Turing
  • Computer Science
    Proc. London Math. Soc.
  • 1937
TLDR
This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.

Grundzüge der theoretischen Logik

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