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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.01176 |
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| _version_ | 1866915556310908928 |
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| author | Zhang, Yilong |
| author_facet | Zhang, Yilong |
| contents | We construct an expansion of a real closed field by a multiplicative subgroup adapting Poizat's theory of green points. Its theory is strongly dependent, and every open set definable in a model of this theory is semialgebraic. We prove that the real field with a dense family of logarithmic spirals, proposed by Zilber, satisfies our theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Green points in the reals Zhang, Yilong Logic 03C64 We construct an expansion of a real closed field by a multiplicative subgroup adapting Poizat's theory of green points. Its theory is strongly dependent, and every open set definable in a model of this theory is semialgebraic. We prove that the real field with a dense family of logarithmic spirals, proposed by Zilber, satisfies our theory. |
| title | Green points in the reals |
| topic | Logic 03C64 |
| url | https://arxiv.org/abs/2501.01176 |