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The ω-consistency of number theory via Herbrand's theorem

Published online by Cambridge University Press:  12 March 2014

W. D. Goldfarb  and
T. M. Scanlon
W. D. Goldfarb
Affiliation:
Society of Fellows, Harvard University, Cambridge, Massachusetts 02138
T. M. Scanlon
Affiliation:
Princeton University, Princeton, New Jersey 08540
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Extract

In this sequel to [7] the method of the consistency proof presented there is extended to provide a proof of the ω-consistency of the systems of number theory which were there shown consistent. This proof yields sharp bounds on the ordinal recursions required to establish the κ-consistency of these systems. The main technical innovation of this proof is the extension of what are essentially the methods of Ackermann [1] for handling finite sets of critical formulae of the first and second kinds to apply as well to sets of critical formulae in which the rank ordering is transfinite. The notation, definitions, and results of [7] will be presupposed throughout; we suggest the reader keep a copy of that paper at hand.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 39 , Issue 4 , December 1974 , pp. 678 - 692
Copyright
Copyright © Association for Symbolic Logic 1974

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References

REFERENCES

[1] Ackermann, W., Zur Widerspruchsfreiheit der Zahlentheorie, Mathematische Annalen, vol. 117 (1940), pp. 162–194.Google Scholar
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