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Palacín, Daniel; Sklinos, Rizos

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

Notre Dame J. Formal Logic 59, No. 2, 157-169 (2018).
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.

Cited in 2 Reviews
Cited in 9 Documents

MSC:

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

Keywords:

superstability; free abelian groups
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\textit{D. Palacín} and \textit{R. Sklinos}, Notre Dame J. Formal Logic 59, No. 2, 157--169 (2018; Zbl 1455.03042)
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