Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-17T17:00:17.858Z Has data issue: false hasContentIssue false

On Lascar rank and Morley rank of definable groups in differentially closed fields

Published online by Cambridge University Press:  12 March 2014

Anand Pillay
Affiliation:
Department of Mathematics, University of Illinois at Urbana Champaign, 273 Altgelt Hall, 1409 West Green Street, Urbana, IL 61801, USA, E-mail: [email protected]
Wai Yan Pong
Affiliation:
Department of Mathematics, University of Illinois at Urbana Champaign, 273 Altgelt Hall, 1409 West Green Street, Urbana, IL 61801, USA, E-mail: [email protected]

Abstract

Morley rank and Lascar rank are equal on generic types of definable groups in differentially closed fields with finitely many commuting derivations.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

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]Berline, Ch. and Lascar, D., Supers table groups, Annals of Pure and Applied Logic, vol. 30 (1986), no. 1, pp. 143.CrossRefGoogle Scholar
[2]Hrushovski, E. and Scanlon, T., Lascar and Morley ranks differ in differentially closed fields, this Journal, vol. 64 (1999), no. 3, pp. 12801284.Google Scholar
[3]Lascar, D., Lesgroupes ω-stables de rang fini, Transactions of the American Mathematical Society, vol. 292 (1985), no. 2, pp. 451462.Google Scholar
[4]McGrail, T., The Model theory of differential fields with finitely many commuting derivations, this Journal, vol. 65 (2000), no. 2, pp. 885913.Google Scholar
[5]Pillay, A., Geometric stability theory, Oxford Logic Guides, vol. 32, Oxford University Press, 1996.CrossRefGoogle Scholar
[6]Pong, W. Y., Some applications of ordinal dimensions to the theory of differentially closedfields, this Journal, vol. 65 (2000), no. 1, pp. 347356.Google Scholar