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arXiv · 1007.0822

The Isomorphism Relation Between Tree-Automatic Structures

Olivier Finkel·Stevo Todorcevic
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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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Olivier Finkel, Stevo Todorcevic. 2010-07-06. The Isomorphism Relation Between Tree-Automatic Structures. https://doi.org/10.2478/s11533-010-0014-7

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