Interpretable fields in various valued fields

FUZZY HYPERVECTOR SPACES OVER VALUED FIELDS

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

Stratifications in Valued Fields

In these notes, I present a new, strong notion of stratifications which describe singularities of sets in Henselian valued fields. In the first part, I give the definition, some examples, and I state the main result about their existence; in the second part, I explain how such a stratification in a valued field induces a classical Whitney stratification in R.

Groups Interpretable in Theories of Fields

We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree

Amalgamating valued fields

Dp-Minimal Valued Fields

We show that dp-minimal valued fields are henselian and give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.