The computable dimension of ordered abelian groups

Abstract

Let G be a computable ordered abelian group. We show that the computable dimension of G is either 1 or ω, that G is computably categorical if and only if it has finite rank, and that if G has only finitely many Archimedean classes, then G has a computable presentation which admits a computable basis. © 2003 Elsevier Science (USA). All rights reserved.