Undecidability of the theory of Abelian groups with an automorphism
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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.
KeywordsAbelian Group Elementary Theory Complete Abelian Group
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