Computable ordered abelian groups and fields

Authors:
Alexander G. Melnikov
Affiliations:
The University of Auckland, New Zealand
Venue:
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Year:
2010

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Recursively enumerable sets and degrees

Recursively enumerable sets and degrees
0˝-Categorical Completely Decomposable Torsion-Free Abelian Groups

CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice

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Abstract

We present transformations of linearly ordered sets into ordered abelian groups and ordered fields. We study effective properties of the transformations. In particular, we show that a linear order L has a Δ20 copy if and only if the corresponding ordered group (ordered field) has a computable copy. We apply these codings to study the effective categoricity of linear ordered groups and fields.