The Isomorphism Relation Between Tree-Automatic Structures

Abstract : An $\omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $\omega$-tree-automatic structures. We prove first that the isomorphism relation for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is neither a $\Sigma_2^1$-set nor a $\Pi_2^1$-set.
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Contributeur : Olivier Finkel <>
Soumis le : lundi 5 juillet 2010 - 17:45:06
Dernière modification le : vendredi 4 janvier 2019 - 17:32:32
Document(s) archivé(s) le : jeudi 7 octobre 2010 - 12:15:23

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Olivier Finkel, Stevo Todorcevic. The Isomorphism Relation Between Tree-Automatic Structures. Central European Journal of Mathematics, Springer Verlag, 2010, 8 (2), p. 299-313. ⟨10.2478/s11533-010-0014-7⟩. ⟨hal-00497724⟩

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