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.
Original language | English |
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Pages (from-to) | 216-222 |
Number of pages | 7 |
Journal | Journal of Symbolic Logic |
Volume | 70 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2005 |
Externally published | Yes |