On Superstable Expansions of Free Abelian Groups

Abstract

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.

References in corpus (2)

• Some remarks on one-basedness
• On the Generic Type of the Free Group

Cited by in corpus (1)

• A new dp-minimal expansion of the integers