18 citations · 50 across the 19 of their papers we have counts for
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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…
Denseness results in the theory of algebraic fields
Sylvy Anscombe, Philip Dittmann, Arno Fehm
We study when the property that a field is dense in its real and p-adic closures is elementary in the language of rings and deduce that all models of the theory of algebraic fields…
A p-adic analogue of Siegel's Theorem on sums of squares
Sylvy Anscombe, Philip Dittmann, Arno Fehm
Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields.…
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…
Approximation theorems for spaces of localities
Sylvy Anscombe, Philip Dittmann, Arno Fehm
The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequival…