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Notes on the stability of separably closed fields1

Published online by Cambridge University Press:  12 March 2014

Carol Wood
Carol Wood*
Affiliation:
Wesleyan University, Middletown, CT 06457
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Abstract

The stability of each of the theories of separably closed fields is proved, in the manner of Shelah's proof of the corresponding result for differentially closed fields. These are at present the only known stable but not superstable theories of fields. We indicate in §3 how each of the theories of separably closed fields can be associated with a model complete theory in the language of differential algebra. We assume familiarity with some basic facts about model completeness [4], stability [7], separably closed fields [2] or [3], and (for §3 only) differential fields [8].

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 44 , Issue 3 , September 1979 , pp. 412 - 416
Copyright
Copyright © Association for Symbolic Logic 1979

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Footnotes

1

Research supported in part by N.S.F. Grant MCS75-08241.

References

REFERENCES

[1]Eršov, Yu. L., Fields with a solvable theory, Doklady Akademii Nauk SSSR, vol. 174(1967), pp. 19–20; English translation, Soviet Mathematics, vol. 8 (1967), pp. 575-576.Google Scholar
[2]Jacobson, N., Lectures in abstract algebra, vol. III, Van Nostrand, Princeton, N. J, 1964.CrossRefGoogle Scholar
[3]Lang, S., Introduction to algebraic geometry, Addison-Wesley, Reading, Massachusetts, 1958.Google Scholar
[4]Robinson, A., An introduction to model theory, North-Holland, Amsterdam, 1965.Google Scholar
[5]Shelah, S., Differentially closed fields, Israel Journal of Mathematics, vol. 16(1973), pp. 314–328.CrossRefGoogle Scholar
[6]Shelah, S., The lazy model-theoretician's guide to stability, Logique et Analyse, vol. 71–72(1975), pp. 241–308.Google Scholar
[7]Shelah, S., Stability, the f.c.p., and superstability, Annals of Mathematical Logic, vol. 3(1971), pp. 271–361.CrossRefGoogle Scholar
[8]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