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On Kueker Simple Theories
The Journal of Symbolic Logic
Vol. 70, No. 1 (Mar., 2005), pp. 216-222
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/27588354
Page Count: 7
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We show that a Kueker simple theory eliminates Ǝ∞ 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.
The Journal of Symbolic Logic © 2005 Association for Symbolic Logic