Skip to main content
Log in

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. A. I. Mal'tsev, “Some questions on the boundary between algebra and logic,” Proceedings of the International Congress of Mathematicians, Moscow, 1966, Mir, Moscow (1968), pp. 217–231.

    Google Scholar 

  2. A. I. Kokorin and V. M. Kopytov, Linearly Ordered Groups [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  3. A. M. Slobodskoi and É. I. Fridman, “Theories of Abelian groups with predicates specifying subgroups,” Algebra Logika,14, No. 5, 572–575 (1975).

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 23, No. 4, pp. 515–520, April, 1978.

The author would like to thank A. I. Kokorin for suggesting this topic and A. G. Pinus for his valuable observations.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mart'yanov, V.I. Undecidability of the theory of Abelian groups with an automorphism. Mathematical Notes of the Academy of Sciences of the USSR 23, 281–284 (1978). https://doi.org/10.1007/BF01786956

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01786956

Keywords

Navigation