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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2311.00411 |
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| _version_ | 1866909160226947072 |
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| author | De Mase, Anna |
| author_facet | De Mase, Anna |
| contents | We investigate the model completeness of the theory of a mixed characteristic henselian valued field with finite ramification relative to the residue field and value group. We address the case in which the valued field has a value group with finite spines, and the case in which the value group is elementarily equivalent to the infinite lexicographic sum of $\mathbb{Z}$ with a minimal positive element. In both cases, we find a one-sorted language in which the theory of the valued field is model complete, if the theory of the residue field is model complete in the language of rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00411 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relative model completeness of henselian valued fields with finite ramification and various value groups De Mase, Anna Logic We investigate the model completeness of the theory of a mixed characteristic henselian valued field with finite ramification relative to the residue field and value group. We address the case in which the valued field has a value group with finite spines, and the case in which the value group is elementarily equivalent to the infinite lexicographic sum of $\mathbb{Z}$ with a minimal positive element. In both cases, we find a one-sorted language in which the theory of the valued field is model complete, if the theory of the residue field is model complete in the language of rings. |
| title | Relative model completeness of henselian valued fields with finite ramification and various value groups |
| topic | Logic |
| url | https://arxiv.org/abs/2311.00411 |