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On Kueker simple theories

  • Ziv Shami (a1)
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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References
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[B]Buechler, S., Kueker's conjecture for superstable theories, this Journal, vol. 49 (1984), pp. 930934.
[H]Hrushovski, E., Kueker's conjecture for stable theories, this Journal, vol. 54 (1989), no. 1.
[K]Kim, B., A note on Lascar strong types in simple theories, this Journal, vol. 63 (1998), pp. 926–36.
[S]Shami, Z., Coordinatization by binding groups and unidimensionality in simple theories, this Journal, vol. 69 (2004), pp. 12211242.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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