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Une fonction de Kolchin pour les corps imparfaits de degré d'imperfection fini

Published online by Cambridge University Press:  12 March 2014

Françoise Delon
Françoise Delon*
Affiliation:
C.N.R.S. et Université Paris7, U.F.R. de Mathematiques, Case 7012. 2 Place Jussieu, 75251 Paris Cedex 5, France, E-mail: delon@logique.jussieu.fr
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Abstract

Non-perfect separably closed fields are stable, and not superstable. As a result, not all types can be ranked. We develop here a new tool, a “semi-rank”, which takes values in the non-negative reals, and gives a sufficient condition for forking of types. This semi-rank is built up from a transcendence function, analogous to the one considered by Kolehin in the context of differentially closed fields. It yields some orthogonality and stratification results.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 664 - 680
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

[1] Baldwin, John, Fundamentals of Stability Theory, Springer-Verlag, Berlin, 1988.Google Scholar
[2] Benoist, Franck, Rungs et types génériques dans les corps différentiellement clos, this Journal, vol. 67 (2002), pp. 1178–1188.Google Scholar
[3] Blossier, Thomas, Ensembles minimaux localement modulaires, Ph.D. thesis, Université Paris 7-Denis Diderot, 2001.Google Scholar
[4] Blossier, Thomas, Subgoups of the additive group of a separably closed field, Annals of Pure and Applied Logic, à paraître.Google Scholar
[5] Bouscaren, Elisabeth and Delon, Françoise, Groups definable in separably closed fields, Transactions of the American Mathematical Society, vol. 354 (2001), pp. 945–966.Google Scholar
[6] Chatzidakis, Zoé, Cherlin, Gregory, Shelah, Saharon, Srour, Gabriel, and Wood, Carol, Orthogonality of types in separably closed fields, Classification Theory, Lecture Notes in Mathematics, vol. 1292, Springer-Verlag, Berlin, 1987.Google Scholar
[7] Chatzidakis, Zoé and Wood, Carol, Minimal types in separably closed fields, this Journal, vol. 65 (2000), pp. 1443–1450.Google Scholar
[8] Delon, Françoise, Idéaux et types sur les corps séparablement clos, Supplément au Bulletin de la Société Mathématique de France, Mémoire 33, vol. 116 (1988).Google Scholar
[9] Delon, Françoise, Separably closed fields, Model Theory and Algebraic Geometry (Bouscaren, E., editor), Lecture Notes in Mathematics, vol. 1696, Springer, Berlin, 1998.Google Scholar
[10] Kolchin, Ellis Robert, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.Google Scholar
[11] Lang, Serge, Algebra, Addison-Wesley Publishing Company, Amsterdam, 1978.Google Scholar
[12] Lascar, Daniel, Stabilité en théorie des modèles, Cabay, Louvain-la-neuve, 1986, ou en version anglaise, Stability in model theory, Longman Scientific & Technical, Harlow 1987.Google Scholar
[13] Pong, Wai Yan, Ordinal dimensions and differential completeness, Ph.D. thesis, University of Illinois, Chicago, 2000.Google Scholar
[14] Pong, Wai Yan, Some applications of ordinal dimensions to the theory of differential closed fields, this Journal, vol. 65 (2000), pp. 347–356.Google Scholar
[15] Shelah, Saharon, Classification Theory, revised ed., North-Holland, New York, 1990.Google Scholar