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The computable dimension of ordered abelian groups
Authors:Sergey S Goncharov
Institution:a Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Russia
b Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA
c Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA
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.
Keywords:03D  06F
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