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Article Dans Une Revue Central European Journal of Mathematics Année : 2010

The Isomorphism Relation Between Tree-Automatic Structures

Résumé

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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Dates et versions

hal-00497724 , version 1 (05-07-2010)

Identifiants

Citer

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