Distality in valued fields and related structures

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.

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.

Valued Difference Fields and Ntp

We show that the theory of the non-standard Frobenius automorphism, acting on an algebraically closed valued field of equal characteristic 0, is NTP2. More generally, in the contractive as well as in the isometric case, we prove that a σ-Henselian valued difference field of equicharacteristic 0 is NTP2, provided both the residue difference field and the value group (as an ordered difference gro...

Linear Problems in Valued Fields

A quantifier elimination procedure for a class M over a language L is an algorithm that given an L-formula φ computes a quantifier-free L-formula φ′ such that M |= φ′ ←→ φ. An L-formula is called linear if it contains no products or reciprocals of quantified variables. Quantifier elimination methods for valued fields have been extensively investigated in the past. The existence of a quantifier ...

Definable Sets in Valued Fields