Constructive Boolean algebras with almost-identical automorphisms (Q1078560)

An automorphism \(\phi\) of a constructive model (B,\(\nu)\) is called recursive if there exists a recursive function f such that \(\phi \nu =\nu f\). Let \(Aut_ r(B,\mu)\) be the group of all recursive automorphisms of (B,\(\mu)\), Fin be the group of all permutations of \(\omega\) which move only a finite number of elements. In Algebra Logika 22, No.2, 138-158 (1983; Zbl 0549.03031) the author proved that for every atomic strongly constructivizable Boolean algebra B there exists a constructivization \(\mu\) such that \(Aut_ r(B,\mu)\cong Fin\). In the present paper he proves that for every infinite atomic constructive Boolean algebra (B,\(\nu)\) there exists a constructivization \(\mu\) such that \(Aut_ r(B,\mu)\cong Fin\).