Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T16:23:31.706Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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]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
[3]Hrushovski, E., A new strongly minimal set, Annals of Pure and Applied Logic, vol. 62 (1993), pp. 147–166.CrossRefGoogle Scholar
[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