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Rings which admit elimination of quantifiers

Published online by Cambridge University Press:  12 March 2014

Chantal Berline
Chantal Berline*
Affiliation:
C.N.R.S., Université de Paris 7, Paris, France
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Abstract

The aim of this paper is to provide an addendum to a paper by Rose with the same title which has appeared in an earlier issue of this Journal [2]. Our new result is:

Theorem. A ring of characteristic zero which admits elimination of quantifiers in the language (0, 1, +, ·) is an algebraically closed field.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 1 , March 1981 , pp. 56 - 58
Copyright
Copyright © Association for Symbolic Logic 1981

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References

REFERENCES

[1]Macintyre, A., On ω1-categorical theories of fields, Fundamenta Mathematicae, vol. 71 (1971), pp. 1–25.CrossRefGoogle Scholar
[2]Rose, B. I., Rings which admit elimination of quantifiers, this Journal, vol. 43 (1978), pp. 92–112.Google Scholar