An Approximate AKE Principle for Metric Valued Fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913068126044160 |
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| author | Hils, Martin Ludwig, Stefan Marian |
| author_facet | Hils, Martin Ludwig, Stefan Marian |
| contents | We study metric valued fields in continuous logic, following Ben Yaacov's approach, thus working in the metric space given by the projective line. As our main result, we obtain an approximate Ax-Kochen-Ershov principle in this framework, completely describing elementary equivalence in equicharacteristic 0 in terms of the residue field and value group. Moreover, we show that, in any characteristic, the theory of metric valued difference fields does not admit a model-companion. This answers a question of Ben Yaacov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10186 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An Approximate AKE Principle for Metric Valued Fields Hils, Martin Ludwig, Stefan Marian Logic 03C66, 03C60 (Primary), 12L10 (Secondary) We study metric valued fields in continuous logic, following Ben Yaacov's approach, thus working in the metric space given by the projective line. As our main result, we obtain an approximate Ax-Kochen-Ershov principle in this framework, completely describing elementary equivalence in equicharacteristic 0 in terms of the residue field and value group. Moreover, we show that, in any characteristic, the theory of metric valued difference fields does not admit a model-companion. This answers a question of Ben Yaacov. |
| title | An Approximate AKE Principle for Metric Valued Fields |
| topic | Logic 03C66, 03C60 (Primary), 12L10 (Secondary) |
| url | https://arxiv.org/abs/2208.10186 |