A hierarchy of tree-automatic structures

@article{Finkel2012AHO,
  title={A hierarchy of tree-automatic structures},
  author={Olivier Finkel and Stevo Todorcevic},
  journal={ArXiv},
  year={2012},
  volume={abs/1111.1504}
}
  • Olivier Finkel, Stevo Todorcevic
  • Published in J. Symb. Log. 2012
  • Mathematics, Computer Science
  • ArXiv
  • We consider $\omega^n$-automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length $\omega^n$ for some integer $n\geq 1$. We show that all these structures are $\omega$-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation for $\omega^2$-automatic (resp. $\omega^n$-automatic for $n>2$) boolean algebras (respectively, partial orders, rings, commutative rings, non… CONTINUE READING

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