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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
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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

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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