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The Isomorphism Relation Between Tree-Automatic Structures

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 نشر من قبل Olivier Finkel
 تاريخ النشر 2010
  مجال البحث الهندسة المعلوماتية
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 تأليف Olivier Finkel




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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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