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The Isomorphism Relation Between Tree-Automatic Structures
Abstract
International audienceAn -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 -tree-automatic structures. We prove first that the isomorphism relation for -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 -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 -set nor a -set- info:eu-repo/semantics/article
- Journal articles
- independence results
- $\omega$-tree-automatic structures
- boolean algebras
- partial orders
- rings
- groups
- isomorphism relation
- models of set theory
- independence results.
- MSC: 03D05; 03E35; 03C52; 03B70
- [MATH.MATH-LO]Mathematics [math]/Logic [math.LO]
- [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]
- [INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]