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Prime model extensions for differential fields of characteristic p ≠ 0

Published online by Cambridge University Press:  12 March 2014

Carol Wood
Carol Wood*
Affiliation:
Yale University, New Haven, Connecticut 06520
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Extract

The main purpose of this paper is to show that there exists a prime differentially closed extension over each differentially perfect field. We do this in a roundabout manner by first giving new and simple axioms for the theory of differentially closed fields (in the manner of Blum [1] for characteristic 0) and by proving that this theory is the model completion of the theory of differentially perfect fields. This paper can be read independently from [10], where we gave more complicated axioms for the same theory (in the manner of Robinson [6] for characteristic 0).

I am indebted to E. R. Kolchin for answering many questions and for making the manuscript of his forthcoming book [2] available to me.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 39 , Issue 3 , September 1974 , pp. 469 - 477
Copyright
Copyright © Association for Symbolic Logic 1974

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References

REFERENCES

[1]Blum, L., Thesis, M.I.T., Cambridge, Mass., 1968.Google Scholar
[2]Kolchin, E. R., Differential algebra and algebraic groups, Academic Press, New York, 1973.Google Scholar
[3]Morley, M., Categoricity in power, Transactions of the American Mathematical Society, vol. 114 (1965), pp. 514–538.CrossRefGoogle Scholar
[4]Ritt, J., Differential algebra, Dover, New York, 1966.Google Scholar
[5]Robinson, A., An introduction to model theory, North-Holland, Amsterdam, 1965.Google Scholar
[6]Robinson, A., On the concept of a differentially closed field, Bulletin of the Research Council of Israel, Section F, vol. 8F (1959), pp. 113–128.Google Scholar
[7]Sacks, G., Saturated model theory, Benjamin, Reading, Mass., 1972.Google Scholar
[8]Seidenberg, A., An elimination theory for differential algebra, University of California Mathematics Publications, vol. 3 (1956), pp. 31–65.Google Scholar
[9]Seidenberg, A., Some basic theorems in differential algebra, Transactions of the American Mathematical Society, vol. 73 (1952), pp. 174–190.Google Scholar
[10]Wood, C., The model theory of differential fields of characteristic p ≠ 0, Proceedings of the American Mathematical Society, vol. 40 (1973), pp. 577–584.Google Scholar
[11]Shelah, S., Differentially closed fields (preprint).Google Scholar