Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-18T18:50:25.103Z Has data issue: false hasContentIssue false
  • English
  • Français

On countable simple unidimensional theories

Published online by Cambridge University Press:  12 March 2014

Anand Pillay
Anand Pillay*
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green St., Urbana, Illinois 61801, USA, E-mail: pillay@.math.uiuc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that any countable simple unidimensional theory T is supersimple, under the additional assumptions that T eliminates hyperimaginaries and that the Dϕ-ranks are finite and definable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1377 - 1384
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, I., Pillay, A., and Vassiliev, E., Lovely pairs of models, to appear in Annals of Pure and Applied Logic.Google Scholar
[2] Hrushovski, E., Countable stable unidimensional theories are superstable, preprint, 1985.Google Scholar
[3] Hrushovski, E., Unidimensional theories are superstable, Annals of Pure and Applied Logic, vol. 50 (1990), pp. 117–138.CrossRefGoogle Scholar
[4] Pillay, A., Geometric stability theory, Oxford University Press, 1996.CrossRefGoogle Scholar
[5] Poizat, B., Paires de structures stables, this Journal, vol. 48 (1983), pp. 234–249.Google Scholar
[6] Shami, Z., Coordinatization by binding groups and unidimensionality in simple theories, to be submitted.Google Scholar
[7] Shami, Z., On Kueker simple theories, submitted to this Journal.Google Scholar
[8] Shelah, S., Classification theory, North-Holland, 1990.Google Scholar
[9] Wagner, F. O., Simple theories, Kluwer, 1999.Google Scholar