The Isomorphism Relation Between Tree-Automatic Structures

An -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 -treeautomatic 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 -treeautomatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n 2) is neither a 1 2-set nor a 1 2-set.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Olivier Finkel, Stevo Todorcevic
• Keywords: -treeautomatic Boolean Algebras, Commutative Rings, CORR 2010, Education, Non Commutative Rings