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A note on a proof of Hilbert's second ε-theorem

Published online by Cambridge University Press:  12 March 2014

Pier Luigi Ferrari
Pier Luigi Ferrari*
Affiliation:
Istituto di Matematica, Università di Genova, Genova, Italy
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Extract

The aim of this short note is to correct an error in the proof in [1], more precisely in Remark 1 on page 395, where it is stated that any improper word has rank ≥2. This claim is false; and, consequently, Remark 2, asserting that any 1,0-deduction does not contain improper Q-terms, also fails immediately. In fact, let us consider the word

It is easily seen that the rank of W is 1, but W is obviously improper. We remark that it is possible, in the same way, to give examples of improper words of rank 1 containing (without subordination) ε-subterms of arbitrarily high rank. In the following section we sketch a corrected version of the proof in order to eliminate all improper ε-terms.

We refer to the notation and definitions of [1]. A more extended description of the theories involved can be found in [2].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 1 , March 1987 , pp. 214 - 215
Copyright
Copyright © Association for Symbolic Logic 1987

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References

REFERENCES

[1] Flannagan, T. B., On an extension of Hilbert's second ε-theorem, this Journal, vol. 40 (1975), pp. 393–397.Google Scholar
[2] Leisenring, A. C., Mathematical logic and Hilbert's ε-symbol, MacDonald, London, 1969.Google Scholar