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Rings which admit elimination of quantifiers

  • Chantal Berline (a1)

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.

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References

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[1]Macintyre, A., On ω1-categorical theories of fields, Fundamenta Mathematicae, vol. 71 (1971), pp. 125.
[2]Rose, B. I., Rings which admit elimination of quantifiers, this Journal, vol. 43 (1978), pp. 92112.

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