10 citations · 30 across the 18 of their papers we have counts for
24 papers
AKE principles in roughly deeply ramified henselian valued fields
Franziska Jahnke, Margarete Ketelsen, Floris Vermeulen
We show that for any henselian valued field of mixed characteristic , the (existential) -theory of the valued field is determined by the (existen…
Definability via the tilting correspondence
Gessica Alecci, Ihsane Hadeg, Franziska Jahnke +2
We show that arithmetic definability of henselian valuations is preserved by the tilting correspondence. Moreover, we show that if a perfectoid valuation is arithmetically definabl…
AKE principles for deeply ramified fields
Franziska Jahnke, Jonas van der Schaaf
We study the model theory of deeply ramified fields of positive characteristic. Generalizing the perfect case treated in work by Jahnke and Kartas on the model theory of perfectoid…
Perfectoid fields in the language of rings
Franziska Jahnke, Ferréol Lavaud
Building on work of the first author and Kartas, we identify the elementary class generated by all perfectoid fields of fixed residue characteristic in the language of rings.
Growing Spines: Ad Infinitum et Ad Infinitesimalia
Blaise Boissonneau, Anna De Mase, Franziska Jahnke +1
We prove that for every ordered abelian group there exists a non-trivial ordered abelian group such that with the lexicographic order, and give a…
Growing Spines Ad Infinitum
Blaise Boissonneau, Anna De Mase, Franziska Jahnke +1
We show that every non-trivial ordered abelian group is augmentable by infinite elements, i.e., we have for some non-trivial ordered abelian group …
Ax-Kochen-Ershov principles for finitely ramified henselian fields
Sylvy Anscombe, Philip Dittmann, Franziska Jahnke
We study the model theory of finitely ramified henselian valued fields of fixed initial ramification, obtaining versions of the Ax-Kochen-Ershov principle as follows. We identify t…
Beyond the Fontaine-Wintenberger theorem
Franziska Jahnke, Konstantinos Kartas
Given a perfectoid field, we find an elementary extension and a henselian defectless valuation on it, whose value group is divisible and whose residue field is an elementary extens…
Definable valuations on ordered fields
Philip Dittmann, Franziska Jahnke, Lothar Sebastian Krapp +1
We study the definability of convex valuations on ordered fields, with a particular focus on the distinguished subclass of henselian valuations. In the setting of ordered fields, o…
Characterizing NIP henselian fields
Sylvy Anscombe, Franziska Jahnke
In this paper, we characterize NIP henselian valued fields modulo the theory of their residue field, both in an algebraic and in a model-theoretic way. Assuming the conjecture that…
The model theory of Cohen rings
Sylvy Anscombe, Franziska Jahnke
The aim of this article is to give a self-contained account of the algebra and model theory of Cohen rings, a natural generalization of Witt rings. Witt rings are only valuation ri…
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…
Recent Progress on Definability of Henselian Valuations
Arno Fehm, Franziska Jahnke
Although the study of the definability of henselian valuations has a long history starting with J. Robinson, most of the results in this area were proven during the last few years.…
When does NIP transfer from fields to henselian expansions?
Franziska Jahnke
Let be an NIP field and let be a henselian valuation on . We ask whether is NIP as a valued field. By a result of Shelah, we know that if is externally defin…
NIP henselian valued fields
Franziska Jahnke, Pierre Simon
We show that any theory of tame henselian valued fields is NIP if and only if the theory of its residue field and the theory of its value group are NIP. Moreover, we show that if $…
Henselianity in the language of rings
Sylvy Anscombe, Franziska Jahnke
We consider four properties of a field related to the existence of (definable) henselian valuations on and on elementarily equivalent fields, and study the implications bet…
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…
Defining coarsenings of valuations
Franziska Jahnke, Jochen Koenigsmann
We study the question which henselian fields admit definable henselian valuations (with or without parameters). We show that every field which admits a henselian valuation with non…
On the quantifier complexity of definable canonical henselian valuations
Arno Fehm, Franziska Jahnke
We discuss definability in the language of rings without parameters of the unique canonical henselian valuation of a field. We show that in most cases where the canonical henselian…
Uniformly defining -henselian valuations
Franziska Jahnke, Jochen Koenigsmann
Admitting a non-trivial -henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, -henselianity is an elem…
Fields with almost small absolute Galois group
Arno Fehm, Franziska Jahnke
We construct and study fields F with the property that F has infinitely many extensions of some fixed degree, but E*/(E*)^n is finite for every finite extension E of F and every n>…
Definable henselian valuations
Franziska Jahnke, Jochen Koenigsmann
In this note we investigate the question whether a henselian valued field carries a non-trivial 0-definable henselian valuation (in the language of rings). It follows from the work…