On a Hierarchy of Groups of Computable Automorphisms

Abstract

Basics and results on groups of computable automorphisms are collected in [1].We recall the main definitions. A computable model

$$\mathfrak{M} = \langle A,f_0^{n_0 } ,...;P_0^{m_0 } ,...\rangle $$

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 $\mathfrak{M}$ which is a computable function on its universe. Allsuch automorphisms form a group denoted by Autc $\mathfrak{M}$.