A hierarchy of tree-automatic structures

@article{Finkel2012AHO,
  title={A hierarchy of tree-automatic structures},
  author={Olivier Finkel and Stevo Todorcevic},
  journal={The Journal of Symbolic Logic},
  year={2012},
  volume={77},
  pages={350 - 368}
}
Abstract We consider ωn-automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length ωn for some integer n ≥ 1. We show that all these structures are ω-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation for ω2-automatic (resp. ωn-automatic for n > 2) boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative… 
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