An Approximate AKE Principle for Metric Valued Fields [Ein approximatives AKE Prinzip für metrisch bewertete Körper]
Hils, Martin; Ludwig, Stefan Marian
Research article in digital collection | PreprintAbstract
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
Details about the publication
Name of the repository: arxiv.org
Article number: 2208.10186
Status: submitted / under review
Release year: 2022
Language in which the publication is written: English
Link to the full text: https://arxiv.org/pdf/2208.10186.pdf
Keywords: valued field; model theory; metric structure; Ax-Kochen-Ershov principle
Authors from the University of Münster
| Hils, Martin | Professorship for Mathematical Logic (Prof. Hils) |
Projects the publication originates from
Duration: 01/01/2020 - 31/12/2024 Funded by: DFG - Individual Grants Programme Type of project: Individual project | |
Duration: 01/01/2019 - 31/12/2025 | 1st Funding period Funded by: DFG - Cluster of Excellence Type of project: Subproject in DFG-joint project hosted at University of Münster |
Vorträge zur Publikation
| An approximate Ax-Kochen-Ershov principle for valued fields in continuous logic Hils, Martin (23/06/2022) Model Theory and Applications 2022, Cetraro Type of talk: scientific talk |