4 papers · 1 filter
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…