5 papers · 1 filter
Decomposing the automorphism group of the surreal numbers
Elliot Kaplan, Lothar Sebastian Krapp, Michele Serra
We study the automorphism group of the field of surreal numbers. Our main structure theorem presents a decomposition of this group into a product of five significant factors. Using…
Ordered henselian valued fields: definability and Borel sets
Lothar Sebastian Krapp, Floris Vermeulen
We firstly show that due to their resplendency ordered henselian valued fields admit relative field quantifier elimination in the Denef--Pas language expanded by linear orders in t…
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…
On Tameness, Measurability and the Independence Property
Lothar Sebastian Krapp, Matthieu Vermeil, Laura Wirth
In the area of Tame Geometry, different model-theoretic tameness conditions are established and their relationships are analyzed. We construct a subfield of the real numbers th…
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…