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Lascar and Morley ranks differ in differentially closed fields

Published online by Cambridge University Press:  12 March 2014

Ehud Hrushovski  and
Thomas Scanlon
Ehud Hrushovski
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel E-mail: ehud@sunset.ma.haji.ac.il
Thomas Scanlon
Affiliation:
Department of Mathematics, University of California, Evans Hall, Berkeley, California 94720, USA E-mail: scanlon@math.berkeley.edu
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Extract

We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We will approach this through the (perhaps) more fundamental issue of the variation of Morley rank in families. We will be interested here only in sets of finite Morley rank. Section 1 consists of some general lemmas relating the above issues. Section 2 points out a family of sets of finite Morley rank, whose Morley rank exhibits discontinuous upward jumps. To make the base of the family itself have finite Morley rank, we use a theorem of Buium.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 3 , September 1999 , pp. 1280 - 1284
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

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