• Publications
  • Influence
On Strongly NIP Ordered Fields and Definable Convex Valuations
We investigate what henselian valuations on ordered fields are definable in the language of ordered rings. This leads towards a systematic study of the class of ordered fields which are dense inExpand
  • 5
  • PDF
Algebraic and Model Theoretic Properties of O-minimal Exponential Fields
An exponential exp on an ordered field (K,+,−, ·, 0, 1, <) is an order-preserving isomorphism from the ordered additive group (K,+, 0, <) to the ordered multiplicative group of positive elements (Expand
  • 1
On Strongly NIP Ordered Fields
The following conjecture is due to Shelah$-$Hasson: Any infinite strongly NIP field is either real closed, algebraically closed, or it admits a non-trivial definable henselian valuation, in theExpand
On Rayner structures
In this note, we study substructures of generalised power series fields induced by families of well-ordered subsets of the group of exponents. We relate set theoretic and algebraic properties of theExpand
Ordered fields dense in their real closure and definable convex valuations
In this paper, we undertake a systematic model and valuation theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselianExpand
  • 1
  • PDF
Schanuel ’ s Conjecture and Exponential Fields
In recent years, Schanuel’s Conjecture has played an important role in Transcendental Number Theory as well as decidability problems in Model Theory. The connection between these two areas was madeExpand
  • 1
  • PDF
Value groups and residue fields of models of real exponentiation
  • L. S. Krapp
  • Mathematics, Computer Science
  • J. Log. Anal.
  • 8 March 2018
TLDR
We give a full characterisation of all triples $(F,G,h) which can be realised in a model of real exponentiation in the following two cases: i) $G$ is countable. ii) $F$ is $\kappa$-saturated for an uncountable regular cardinal. Expand
  • 1
  • PDF
Strongly NIP almost real closed fields
The following conjecture is due to Shelah-Hasson: Any infinite strongly NIP field is either real closed, algebraically closed, or admits a non-trivial definable henselian valuation, in the languageExpand
  • 2
  • PDF