AN APPROXIMATE AKE PRINCIPLE FOR METRIC VALUED FIELDS
Abstract
Abstract 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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Journal of Symbolic Logic
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–23
- Publication date
- 27 April 2026
- Language
- EN