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DMP in strongly minimal sets

Published online by Cambridge University Press:  12 March 2014

Assaf Hasson  and
Ehud Hrushovski
Assaf Hasson
Affiliation:
Mathematical Institute Oxford University, Oxford, UK, E-mail: hasson@maths.ox.ac.uk, URL: http://www.maths.ox.ac.uk/~hasson/
Ehud Hrushovski
Affiliation:
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel, E-mail: ehud@math.huji.ac.il
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Abstract

We construct a strongly minimal set which is not a finite cover of one with DMP. We also show that for a strongly minimal theory T, generic automorphisms exist iff T has DMP, thus proving a conjecture of Kikyo and Pillay.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 1019 - 1030
Copyright
Copyright © Association for Symbolic Logic 2007

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References

REFERENCES

[1]Hasson, A., Interpreting structures of finite Morley Rank in strongly minimal structures, Preprint, 2003.Google Scholar
[2]Hrushovski, E., Strongly minimal expansions of algebraically closed fields, Israel Journal of Mathematics, vol. 79 (1992), pp. 129–151.CrossRefGoogle Scholar
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[4]Kikyo, H. and Pillay, A., The definable multiplicity property and generic automorphisms, Annals of Pure and Applied Logic, vol. 106 (2000), pp. 263–273.CrossRefGoogle Scholar