Automorphisms of Boolean algebras which are recursive over atoms (Q1307158)

The author studies the groups of recursive automorphisms of constructive Boolean algebras that are recursive over atoms. In particular, he proves that if two constructive Boolean algebras have isomorphic groups of automorphisms recursive over atoms then these algebras are isomorphic. A counterexample constructed in the article shows that this result cannot be improved. As a corollary, the author derives that the group of automorphisms recursive over atoms and the group of recursive automorphisms of a Boolean algebra can be different.