Valued difference fields and NTP2

Multiplicative valued difference fields

The theory of valued difference fields (K,σ, v) depends on how the valuation v interacts with the automorphism σ. Two special cases have already been worked out the isometric case, where v(σ(x)) = v(x) for all x ∈ K, has been worked out by Luc Belair, Angus Macintyre and Thomas Scanlon; and the contractive case, where v(σ(x)) > nv(x) for all x ∈ K× with v(x) > 0 and n ∈ N, has been worked out b...

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...

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.

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.