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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2403.17478 |
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| _version_ | 1866909228561596416 |
|---|---|
| author | Johnson, Will |
| author_facet | Johnson, Will |
| contents | We show that C-minimal fields (i.e., C-minimal expansions of ACVF) have the exchange property, answering a question of Haskell and Macpherson. Additionally, we strengthen some theorems of Cubides Kovacsics and Delon on C-minimal fields. First, we show that definably complete C-minimal fields of characteristic 0 have generic differentiability. Second, we show that if the induced structure on the residue field is a pure ACF, then polynomial boundedness holds. In fact, polynomial boundedness can only fail if there are unexpected definable automorphisms of the multiplicative group of the residue field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | C-minimal fields have the exchange property Johnson, Will Logic 03C60 We show that C-minimal fields (i.e., C-minimal expansions of ACVF) have the exchange property, answering a question of Haskell and Macpherson. Additionally, we strengthen some theorems of Cubides Kovacsics and Delon on C-minimal fields. First, we show that definably complete C-minimal fields of characteristic 0 have generic differentiability. Second, we show that if the induced structure on the residue field is a pure ACF, then polynomial boundedness holds. In fact, polynomial boundedness can only fail if there are unexpected definable automorphisms of the multiplicative group of the residue field. |
| title | C-minimal fields have the exchange property |
| topic | Logic 03C60 |
| url | https://arxiv.org/abs/2403.17478 |