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| Main Author: | |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2001.11480 |
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| _version_ | 1866910760066613248 |
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| author | Alouf, Eran |
| author_facet | Alouf, Eran |
| contents | 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} $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_11480 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On dp-minimal expansions of the integers Alouf, Eran Logic 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} $. |
| title | On dp-minimal expansions of the integers |
| topic | Logic |
| url | https://arxiv.org/abs/2001.11480 |