On Kueker simple theories

Journal of Symbolic Logic 70 (1):216-222 (2005)

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.
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DOI http://projecteuclid.org/euclid.jsl/1107298516
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