• Corpus ID: 8518142

Lectures on Jacques Herbrand as a Logician

@article{Wirth2009LecturesOJ,
  title={Lectures on Jacques Herbrand as a Logician},
  author={Claus-Peter Wirth and J{\"o}rg H. Siekmann and Christoph Benzm{\"u}ller and Serge Autexier},
  journal={ArXiv},
  year={2009},
  volume={abs/0902.4682}
}
We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand's Modus Ponens Elimination. Besides Herbrand's Fundamental Theorem and its… 
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References

SHOWING 1-10 OF 282 REFERENCES
Herbrand-Style Consistency Proofs
Only Two Letters: The Correspondence between Herbrand and Gödel
  • W. Sieg
  • Philosophy
    Bulletin of Symbolic Logic
  • 2005
TLDR
Together, the letters reflect broader intellectual currents of the time: they are intimately linked to the discussion of the incompleteness theorems and their potential impact on Hilbert's Program.
The Löwenheim-Skolem Theorem, Theories of Quantification, and Proof Theory
Warren Goldfarb (1971, p. 17) wrote that “Herbrand’s work had an immediate impact on the Hilbert school,” and quotes Paul Bernays (Hilbert and Bernays, 1934, 1939, vol. 1, “Foreword”) to the effect…
Finiteness Theorems in Arithmetic: An Application of Herbrand's Theorem For Σ2 - Formulas
Kreisel’s “unwinding” program
Through his own contributions (individual and collaborative) and his extraordinary personal influence, Georg Kreisel did perhaps more than anyone else to promote the development of proof theory and…
An introduction to mathematical logic and type theory - to truth through proof
TLDR
This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory
TLDR
The Herbrand-Gentzen Theorem will be applied to generalize Beth's results from primitive predicate symbols to arbitrary formulas and terms, showing that the expressive power of each first-order system is rounded out, or the system is functionally complete.
A Supplement to Herbrand
In [5] it was shown that to complete Herbrand's argument for his Fundamental Theorem (see [6]) a weak analyzing function for certain applications of the rules of passage is needed. The following…
On the Interpretation of Non-Finitist Proofs - Part I
  • G. Kreisel
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1951
1. The purpose of the present paper is to formulate the problem of non-finitist proofs, and to solve it for certain extensions of the predicate calculus, and for analysis with the exclusion of the…
The Consistency of Number Theory Via Herbrand's Theorem
TLDR
This proof yields sharp bounds on the ordinal recursions required to establish the κ -consistency of these systems of number theory, and the main technical innovation of this proof is the extension of what are essentially the methods of Ackermann for handling finite sets of critical formulae of the first and second kinds to apply as well to sets of Critical Formula in which the rank ordering is transfinite.
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