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