Universally defining $\mathbb{Z}$ in $\mathbb{Q}$ with $10$ quantifiers
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917580030083072 |
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| author | Daans, Nicolas |
| author_facet | Daans, Nicolas |
| contents | We show that for a global field $K$, every ring of $S$-integers has a universal first-order definition in $K$ with $10$ quantifiers. We also give a proof that every finite intersection of valuation rings of $K$ has an existential first-order definition in $K$ with $3$ quantifiers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02107 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universally defining $\mathbb{Z}$ in $\mathbb{Q}$ with $10$ quantifiers Daans, Nicolas Number Theory 11U99 (Primary) 11U05, 11R52 (Secondary) We show that for a global field $K$, every ring of $S$-integers has a universal first-order definition in $K$ with $10$ quantifiers. We also give a proof that every finite intersection of valuation rings of $K$ has an existential first-order definition in $K$ with $3$ quantifiers. |
| title | Universally defining $\mathbb{Z}$ in $\mathbb{Q}$ with $10$ quantifiers |
| topic | Number Theory 11U99 (Primary) 11U05, 11R52 (Secondary) |
| url | https://arxiv.org/abs/2301.02107 |