This article is cited in 1 paper

Undecidability of the theory of Abelian groups with an automorphism

V. I. Mart'yanov

Irkutsk State University

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 $\langle+,\alpha(x)=y\rangle$, where + is addition and $\alpha(x)=y$ is an automorphism of the (ordered) Abelian group.

UDC: 519.4

Received: 04.01.1977

 English version: Mathematical Notes, 1978, 23:4, 281–284

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