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arXiv · 2001.11480

On dp-minimal expansions of the integers

Eran Alouf
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Abstract

We show that if $ \mathcal{Z} $ is a dp-minimal expansion of $ \left(\mathbb{Z},+,0,1\right) $ that defines an infinite subset of $ \mathbb{N} $, then $ \mathcal{Z} $ is interdefinable with $ \left(\mathbb{Z},+,0,1, < \right) $. As a corollary, we show the same for dp-minimal expansions of $ \left(\mathbb{Z},+,0,1\right) $ which do not eliminate $ \exists^{\infty} $.

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Eran Alouf. 2020-01-30. On dp-minimal expansions of the integers. https://arxiv.org/abs/2001.11480

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