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.
"On Kueker simple theories." J. Symbolic Logic 70 (1) 216 - 222, March 2005. https://doi.org/10.2178/jsl/1107298516