Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T04:49:58.156Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected], URL: http://www.logique.jussieu.fr/www.pezz
Get access Rights & Permissions [Opens in a new window]

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

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] 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