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A supplement to Herbrand

Published online by Cambridge University Press:  12 March 2014

Burton Dreben  and
John Denton
Burton Dreben
Affiliation:
Harvard University McGill University
John Denton
Affiliation:
Harvard University McGill University
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Extract

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 theorem describes such a function. (We use the terminology and notation of [5] except that, for each schema S and each p ≧ 1, we shall write D(S,p) rather than DSp for the domain of order p generated by S. In addition, we shall say that an element of D(S, p) is of order k, 1 ≦ k ≦ p, if it belongs to D(S, k) but not to D(S,k—1).)

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 393 - 398
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Ackermann, W., Zur Widerspruchfreiheit der reinen Zahlentheorie, Mathematische Annalen, vol. 117 (1940), pp. 162–194.CrossRefGoogle Scholar
[2]Denton, J., Applications of the Herbrand theorem, Ph. D. Thesis, Harvard University (1963).Google Scholar
[3]Dreben, B., Corrections to Herbrand, Notices American Mathematical Society, vol. 10 (1963), p. 285.Google Scholar
[4]Dreben, B. and Aanderaa, S., Herbrand analyzing functions, Bulletin American Mathematical Society, vol. 70 (1964), pp. 697–698.CrossRefGoogle Scholar
[5]Dreben, B., Andrews, P., and Aanderaa, S., False lemmas in Herbrand, Bulletin American Mathematical Society, vol. 69 (1963), pp. 699–706.CrossRefGoogle Scholar
[6]Herbrand, J., Recherches sur la théorie de la démonstration, Travaux de la Société des Sciences et des Lettres de Varsovie, Classe III sciences mathématiques et physiques, no. 33 (1930).Google Scholar
[7]Herbrand, J., Sur le problème fondamental de la logique mathématique, Comptes Rendus des séances de la Société des Sciences et des Lettres de Varsovie, Classe III sciences mathématiques et physiques, no. 24 (1931).Google Scholar
[8]Hilbert, D. and Bernays, P., Grundlagen der Mathematik, II, Berlin, 1939.Google Scholar
[9]Wang, H., A Survey of Mathematical Logic, Peking, 1962.Google Scholar