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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