7 papers
Existential fragments of theories of henselian valued fields
Sylvy Anscombe, Arno Fehm
We study fragments of the existential theory of henselian valued fields with parameters. This includes the -fragment in the equicharacteristic or unramified mixed charac…
Linear theories of global fields with absolute values
Arno Fehm, Pierre Touchard
We study the theory of a global field k as a k-vector space with a predicate for one of the absolute values on k. For example, we prove that in this language a global field with an…
On the existential theory of the completions of a global field
Philip Dittmann, Arno Fehm
We discuss the common existential theory of all or almost all completions of a global function field.
Universal-existential theories of fields
Sylvy Anscombe, Arno Fehm
We study various universal-existential fragments of first-order theories of fields, in particular of function fields and of equicharacteristic henselian valued fields. For example…
Hilbert properties of varieties
Arno Fehm, Ariyan Javanpeykar
This is a survey of results on the Hilbert property of algebraic varieties, and variants of it.
Existential rank and essential dimension of diophantine sets
Nicolas Daans, Philip Dittmann, Arno Fehm
We study the minimal number of existential quantifiers needed to define a diophantine set over a field and relate this number to the essential dimension of the functor of points as…