Order-topological characterization of groups and fields with automatic $\emptyset$-definability
De Anna De Mase
Apparaît dans la collection : Arithmetic of fields: model theory, valuations, and geometry / L'arithmétiques des corps : théories des modèles, valuations, et geometrie
An ordered abelian group G (resp. a field k) has automatic (0)-definability if, in every henselian valued field with value group G (resp. residue field k), the valuation is (0)-definable in the language of rings. In joint work with B. Boissonneau, F. Jahnke, and P. Touchard, we characterize such groups via the model-theoretic properties of weak and strong augmentability by infinitesimals, and such fields via t-henselianity, in characteristic 0. In this talk, I show that strong augmentability admits an order-topological formulation, and I discuss analogous questions for weak augmentability and t-henselianity in the setting of orderable fields. The talk includes results from this joint work, as well as ongoing work with L. S. Krapp and S. Kuhlmann.
