An Approximate AKE Principle for Metric Valued Fields [Ein approximatives AKE Prinzip für metrisch bewertete Körper]
Hils, Martin; Ludwig, Stefan Marian
Forschungsartikel in Online-Sammlung | Preprint | Peer reviewedZusammenfassung
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 zur Publikation
Name des Repositoriums: arxiv.org
Artikelnummer: 2208.10186
Status: eingereicht / in Begutachtung
Veröffentlichungsjahr: 2022
Sprache, in der die Publikation verfasst ist: Englisch
Link zum Volltext: https://arxiv.org/pdf/2208.10186.pdf
Stichwörter: valued field; model theory; metric structure; Ax-Kochen-Ershov principle
Autor*innen der Universität Münster
| Hils, Martin | Professur für Mathematische Logik (Prof. Hils) |