Franziska Jahnke
University of Münster
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Featured researches published by Franziska Jahnke.
Journal of Symbolic Logic | 2017
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-trivial definable henselian valuation. We give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.
Journal of Symbolic Logic | 2015
Franziska Jahnke; Jochen Koenigsmann
In this note we investigate the question when a henselian valued field carries a nontrivial ∅-definable henselian valuation (in the language of rings). This is clearly not possible when the field is either separably or real closed, and, by the work of Prestel and Ziegler, there are further examples of henselian valued fields which do not admit a ∅-definable nontrivial henselian valuation. We give conditions on the residue field which ensure the existence of a parameter-free definition. In particular, we show that a henselian valued field admits a nontrivial henselian ∅-definable valuation when the residue field is separably closed or sufficiently nonhenselian, or when the absolute Galois group of the (residue) field is nonuniversal.
Annals of Pure and Applied Logic | 2015
Franziska Jahnke; Jochen Koenigsmann
Admitting a non-trivial
Mathematical Logic Quarterly | 2015
Arno Fehm; Franziska Jahnke
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arXiv: Logic | 2017
Franziska Jahnke; Jochen Koenigsmann
-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity,
Annals of Pure and Applied Logic | 2018
Sylvy Anscombe; Franziska Jahnke
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Mathematical Logic Quarterly | 2015
Immanuel Halupczok; Franziska Jahnke
-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable
Israel Journal of Mathematics | 2016
Arno Fehm; Franziska Jahnke
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arXiv: Logic | 2016
Franziska Jahnke; Pierre Simon
-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical
arXiv: Logic | 2018
Yatir Halevi; Assaf Hasson; Franziska Jahnke
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