The Isomorphism Problem on Classes of Automatic Structures

Several new undecidability results on isomorphism problems for automatic structures are shown: (i) The isomorphism problem for automatic equivalence relations is Π
₁
⁰
-complete, (ii) The isomorphism problem for automatic trees of height n ≥ 2 is Π
_2n-3
⁰
-complete, (iii) The isomorphism problem for automatic linear orders is not arithmetical.