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The independence relation in separably closed fields

Published online by Cambridge University Press:  12 March 2014

G. Srour
G. Srour*
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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Abstract

We give an alternative proof of the stability of separably closed fields of fixed Éršov invariant to the one given in [W]. We show that in case the Éršov invariant is finite, the theory is in fact equational. We also characterize the independence relation in those theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 51 , Issue 3 , September 1986 , pp. 715 - 725
Copyright
Copyright © Association for Symbolic Logic 1986

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References

REFERENCES

[B]Baldwin, J. T., Stability theory (book in preparation).Google Scholar
[E]Éršov, Ú. L., Fields with a solvable theory, Doklady Akadéemii Nauk SSSR,vol. 174 (1967), pp. 19–20; English translation, Soviet Mathematics, vol. 8 (1967), pp. 575–576.Google Scholar
[LP]Lascar, D. and Poizat, B., Introduction to forking, this Journal, vol. 44 (1979), pp. 330–350.Google Scholar
[M]Makkai, M., A survey of basic stability theory, with particular emphasis on orthogonality and regular types, Israel Journal of Mathematics, vol. 49 (1984), pp. 181–238.CrossRefGoogle Scholar
[P]Pillay, A., Introduction to stability theory, Oxford University Press, Oxford, 1983.Google Scholar
[PS]Pillay, A. and Srour, G., Closed sets and chain conditions in stable theories, this Journal, vol. 49 (1984), pp. 1350–1362.Google Scholar
[S]Srour, G., Equations and equational theories, Ph.D. thesis, McGill University, Montréal, 1984.Google Scholar
[W]Wood, C., Notes on the separability of separably closed fields, this Journal, vol. 44 (1979), pp. 412–416.Google Scholar