Model-theoretic complexity of automatic structures

@article{Khoussainov2009ModeltheoreticCO,
  title={Model-theoretic complexity of automatic structures},
  author={Bakhadyr Khoussainov and Mia Minnes},
  journal={Ann. Pure Appl. Log.},
  year={2009},
  volume={161},
  pages={416-426}
}
We study the complexity of automatic structures via well-established concepts from both logic and model theory, including ordinal heights (of well-founded relations), Scott ranks of structures, and Cantor-Bendixson ranks (of trees). We prove the following results: 1) The ordinal height of any automatic well-founded partial order is bounded by ωω; 2) The ordinal heights of automatic well-founded relations are unbounded below (ω1CK ; 3) For any infinite computable ordinal α, there is an automatic… Expand
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