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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: zshami@math.uiuc.edu
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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

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References

REFERENCES

[B]Buechler, S., Kueker's conjecture for superstable theories, this Journal, vol. 49 (1984), pp. 930–934.Google Scholar
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[S]Shami, Z., Coordinatization by binding groups and unidimensionality in simple theories, this Journal, vol. 69 (2004), pp. 1221–1242.Google Scholar