Computable valued fields

Computable Algebra, General Theory and Theory of Computable Fields(1)

Introduction. Abstract algebra is the product of a transition from such concrete systems as the ring of integers or the field of rational numbers to the corresponding, axiomatically defined, abstract systems. In the course of this abstraction process various properties of the concrete system are lost. The field of rational numbers, for example, possesses a natural topology, an ordering, and fur...

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.

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...