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Discouraging results for ultraimaginary independence theory

Published online by Cambridge University Press:  12 March 2014

Itay Ben-Yaacov
Itay Ben-Yaacov*
Affiliation:
Équipe de Logique Mathématique, UFR de Mathématiques (Case 7012), Université Paris7, 2 Place Jussieu, 75251 Paris Cedex 05, France, E-mail: pezz@logique.jussieu.fr, URL: http://www.logique.jussieu.fr/www.pezz
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Abstract

Dividing independence for ultraimaginaries is neither symmetric nor transitive. Moreover, any notion of independence satisfying certain axioms (weaker than those for independence in a simple theory) and denned for all ultraimaginary sorts, is necessarily trivial.

Keywords

dividingindependenceultraimaginaries
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 3 , September 2003 , pp. 846 - 850
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[1] Ben-Yaacov, Itay, Tomašić, Ivan, and Wagner, Frank O., Constructing an almost hyperdefinable group, preprint, 2001.Google Scholar
[2] Hart, Bradd, Kim, Byunghan, and Pillay, Anand, Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), pp. 293–309.Google Scholar
[3] Kim, Byunghan, Forking in simple unstable theories, Journal of the London Mathematical Society, vol. 57 (1998), no. 2, pp. 257–267.Google Scholar
[4] Kim, Byunghan, Simplicity, and stability in there, this Journal, vol. 66 (2001), pp. 822–836.Google Scholar
[5] Wagner, Frank O., Simple theories, Kluwer Academic Publishers, 2000.Google Scholar