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.
J. Symbolic Logic
70(1):
216-222
(March 2005).
DOI: 10.2178/jsl/1107298516
ACCESS THE FULL ARTICLE
It is not available for individual sale.
This article is only available to subscribers.
It is not available for individual sale.
It is not available for individual sale.