3 papers
math.LO2026
Definable ranks
Lothar Sebastian Krapp, Salma Kuhlmann, Lasse Vogel
We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an order…
math.LO2025
Know Your Rank!
Blaise Boissonneau, Lasse Vogel
We study definable ranks of ordered fields, ordered abelian groups, and linear orders. For an arbitrary linear order , we construct an ordered abelian group with archimedia…
math.LO2024
Definable henselian valuations on dp-minimal real fields
Lothar Sebastian Krapp, Salma Kuhlmann, Lasse Vogel
We give an explicit algebraic characterisation of all definable henselian valuations on a dp-minimal real field. Additionally we characterise all dp-minimal real fields that admit…