Automorphisms of constructivizations of Boolean algebras
Theorem 1.1. Let \(\mu\) be a constructivization of a Boolean algebra \({\mathcal B}\), and suppose that the sets \(\mu^{-1}(the\) atoms of \({\mathcal B})\), \(\mu^{-1}(the\) atomic elements of \({\mathcal B})\), \(\mu^{-1}(the\) atomless elements of \({\mathcal B})\) are recursive. Then, for any constructivization \(\nu\) of \({\mathcal B}\), if the groups of \(\mu\)-recursive and \(\nu\)-recursive automorphisms of \({\mathcal B}\) coincide, then \(\nu\) is recursively equivalent to \(\mu\). Further, there are some results on (i) atomic constructive Boolean algebras in which every recursive automorphism moves only finitely many atoms, and (ii) the dependence of the \(\nu\)-recursive automorphism groups on \(\nu\) (e.g. they can all be conjugated in Aut(\({\mathcal B})\) with the trivial intersection). The paper is the continuation and an improvement of the author's paper in Algebra Logika 22, No.2, 138-158 (1983; Zbl 0549.03031), but can mostly be read independently. However, an acquaintance with \textit{Yu. L. Ershov}'s ''Decision problems and constructivizable models'' (in Russian) (1980; Zbl 0495.03009) is assumed.
recursive equivalence of constructivizations
scientific article; zbMATH DE number 3991487