Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T03:44:03.605Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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