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Conference on Computability in Europe

CiE 2010: Programs, Proofs, Processes pp 321–330Cite as

Computable Ordered Abelian Groups and Fields

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6158))

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 \(\Delta_2^0\) 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.

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Author information

Authors and Affiliations

  1. The University of Auckland, New Zealand

    Alexander G. Melnikov

Authors
  1. Alexander G. Melnikov
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Fernando Ferreira

  2. Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, P.O. Box 94242, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  3. Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, María de Luna 1, 50018, Zaragoza, Spain

    Elvira Mayordomo

  4. Universidade dos Açores, Campus de Ponta Delgada, Apartado 1422, 9501-801, Ponta Delgada, Açores, Portugal

    Luís Mendes Gomes

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Melnikov, A.G. (2010). Computable Ordered Abelian Groups and Fields. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_36

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  • DOI: https://doi.org/10.1007/978-3-642-13962-8_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13961-1

  • Online ISBN: 978-3-642-13962-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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