4 papers
Definable V-topologies, Henselianity and NIP
Yatir Halevi, Assaf Hasson, Franziska Jahnke
We initiate the study of definable V-topolgies and show that there is at most one such V-topology on a t-henselian NIP field. Equivalently, we show that if is a bi-va…
A Conjectural Classification of Strongly Dependent Fields
Yatir Halevi, Assaf Hasson, Franziska Jahnke
We survey the history of Shelah's conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that t…
Dp-minimal valued fields
Franziska Jahnke, Pierre Simon, Erik Walsberg
We show that dp-minimal valued fields are henselian and that a dp-minimal field admitting a definable type V topology is either real closed, algebraically closed or admits a non-tr…
A definable henselian valuation with high quantifier complexity
Immanuel Halupczok, Franziska Jahnke
We give an example of a parameter-free definable henselian valuation ring which is neither definable by a parameter-free -formula nor by a parameter-free $\exists\f…