Undecidability of the theory of Abelian groups with an automorphism

  • V. I. Mart'yanov


We prove undecidability of the elementary theories of: 1) (torsion-free) Abelian groups; 2) (Archimedean) ordered Abelian groups; 3) complete Abelian groups in the signature 〈+,α (x) =y〉, where + is addition and α(x) = y is an automorphism of the (ordered) Abelian group.


Abelian Group Elementary Theory Complete Abelian Group 
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Literature cited

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    Yu. L. Ershov, “Undecidability of certain fields,” Dokl. Akad. Nauk SSSR,161. No. 1, 27–29 (1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • V. I. Mart'yanov
    • 1
  1. 1.Irkutsk State UniversityUSSR

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