Computable Ordered Abelian Groups and Fields

  • Alexander G. Melnikov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6158)


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 \(\Delta_2^0\) 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.


computable algebra effective categoricity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alexander G. Melnikov
    • 1
  1. 1.The University of AucklandNew Zealand

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