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Notes on the stability of separably closed fields1

  • Carol Wood (a1)

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].

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

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[1]Eršov Yu. L., Fields with a solvable theory, Doklady Akademii Nauk SSSR, vol. 174(1967), pp. 1920; English translation, Soviet Mathematics, vol. 8 (1967), pp. 575-576.
[2]Jacobson N., Lectures in abstract algebra, vol. III, Van Nostrand, Princeton, N. J, 1964.
[3]Lang S., Introduction to algebraic geometry, Addison-Wesley, Reading, Massachusetts, 1958.
[4]Robinson A., An introduction to model theory, North-Holland, Amsterdam, 1965.
[5]Shelah S., Differentially closed fields, Israel Journal of Mathematics, vol. 16(1973), pp. 314328.
[6]Shelah S., The lazy model-theoretician's guide to stability, Logique et Analyse, vol. 71–72(1975), pp. 241308.
[7]Shelah S., Stability, the f.c.p., and superstability, Annals of Mathematical Logic, vol. 3(1971), pp. 271361.
[8]Wood C., The model theory of differential fields of characteristic p ≠ 0, Proceedings of the American Mathematical Society, vol. 40(1973), pp. 577584.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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