Automorphisms of constructivizations of Boolean algebras
type: Item
instance of: scholarly article
title: Automorphisms of constructivizations of Boolean algebras
zbMATH Open document ID: 0613.03017
DOI: 10.1007/BF00971303
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03D45
Mathematics Subject Classification ID: 06E99
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 03C57
zbMATH DE Number: 3991487
zbMATH Keywords: group of recursive automorphisms
zbMATH Keywords: recursive equivalence of constructivizations
zbMATH Keywords: simplicity of automorphism groups
zbMATH Keywords: atomic constructive Boolean algebras
author: Andrei S. Morozov
MaRDI profile type: Publication
cites work: Recursive Boolean algebras with recursive atoms
cites work: The Algebraic Simplicity of Certain Groups of Homeomorphisms
full work available at URL: https://doi.org/10.1007/bf00971303
OpenAlex ID: W1984118671
description: scientific article; zbMATH DE number 3991487