Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-22T20:47:14.150Z Has data issue: false hasContentIssue false
  • English
  • Français

On Kueker simple theories

Published online by Cambridge University Press:  12 March 2014

Ziv Shami
Ziv Shami*
Affiliation:
Department of Mathematics, University of Illinois at Urbana Champaign, Urbana, Illinois 61801, USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that a Kueker simple theory eliminates ∃∞ and densely interprets weakly minimal formulas. As part of the proof we generalize Hrushovski's dichotomy for almost complete formulas to simple theories. We conclude that in a unidimensional simple theory an almost-complete formula is either weakly minimal or trivially-almost-complete. We also observe that a small unidimensional simple theory is supersimple of finite SU-rank.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 1 , March 2005 , pp. 216 - 222
Copyright
Copyright © Association for Symbolic Logic 2005

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

[B]Buechler, S., Kueker's conjecture for superstable theories, this Journal, vol. 49 (1984), pp. 930–934.Google Scholar
[H]Hrushovski, E., Kueker's conjecture for stable theories, this Journal, vol. 54 (1989), no. 1.Google Scholar
[K]Kim, B., A note on Lascar strong types in simple theories, this Journal, vol. 63 (1998), pp. 926–36.Google Scholar
[S]Shami, Z., Coordinatization by binding groups and unidimensionality in simple theories, this Journal, vol. 69 (2004), pp. 1221–1242.Google Scholar