On a Hierarchy of Groups of Computable Automorphisms

Basics and results on groups of computable automorphisms are collected in 1].We recall the main definitions. A computable model is a model in which A is a computable subset of the set ! of natural numbers, the mappings i 7! ni(the number of arguments of fi) and i mi (the number of arguments of Pi) are computable, andall operations fi and predicates Pi are computable uniformly in i. A computable automorphism ofa computable model M is an automorphism of which is a computable function on its universe. Allsuch automorphisms form a group denoted by Autc .