An Approximate AKE Principle for Metric Valued Fields - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

An Approximate AKE Principle for Metric Valued Fields

Résumé

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.
Fichier principal
Vignette du fichier
An_Approximate_AKE_Principle_for_Metric_Valued_Fields.pdf (471.43 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03959842 , version 1 (27-01-2023)

Identifiants

Citer

Martin Hils, Stefan Marian Ludwig. An Approximate AKE Principle for Metric Valued Fields. 2022. ⟨hal-03959842⟩
10 Consultations
7 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More