On superstable expansions of free abelian groups. (English) Zbl 1455.03042

Summary: We prove that \((\mathbb{Z},+,0)\) has no proper superstable expansions of finite Lascar rank. Nevertheless, this structure equipped with a predicate defining powers of a given natural number is superstable of Lascar rank \(\omega\). Additionally, our methods yield other superstable expansions such as \((\mathbb{Z},+,0)\) equipped with the set of factorial elements.


03C45 Classification theory, stability, and related concepts in model theory
03C60 Model-theoretic algebra
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