Computable categoricity of the Boolean algebra b(omega) with a distinguished automorphism

Abstract

It is proved that every computably enumerable Turing degree is a degree of categoricity of some computable Boolean algebra with a distinguished automorphism. We construct an example of a computably categorical Boolean algebra with a distinguished automorphism, having a set of atoms in a given computably enumerable Turing degree.

Keywords

• Boolean algebra with distinguished automorphism
• computable categoricity
• categoricity spectrum