There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910592487391232 |
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| author | Fujita, Masato |
| author_facet | Fujita, Masato |
| contents | There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence. In this paper, we prove this assertion and the following more general assertion: Let $\mathcal R$ be either the ordered $\mathbb R$-vector space structure over $\mathbb R$ or the ordered group of reals. A first-order expansion of $\mathcal R$ by a countable subset $D$ of $\mathbb R$ and a compact subset $E$ of $\mathbb R$ of finite Cantor-Bendixson rank is d-minimal if $(\mathcal R,D)$ is locally o-minimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12883 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence Fujita, Masato Logic 03C64 There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence. In this paper, we prove this assertion and the following more general assertion: Let $\mathcal R$ be either the ordered $\mathbb R$-vector space structure over $\mathbb R$ or the ordered group of reals. A first-order expansion of $\mathcal R$ by a countable subset $D$ of $\mathbb R$ and a compact subset $E$ of $\mathbb R$ of finite Cantor-Bendixson rank is d-minimal if $(\mathcal R,D)$ is locally o-minimal. |
| title | There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence |
| topic | Logic 03C64 |
| url | https://arxiv.org/abs/2408.12883 |