The isomorphism relation between tree-automatic Structures
TL;DR: It is proved that the isomorphism relation for ω-tree-automatic boolean algebras is not determined by the axiomatic system ZFC and is neither a Σ21- set nor a Π21-set.
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Abstract: An ω-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 ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is neither a Σ21-set nor a Π21-set.
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