18 citations · 50 across the 19 of their papers we have counts for
22 papers
Elimination results for tame fields with finite residue fields
Sylvy Anscombe, Blaise Boissonneau
Building on work of Kuhlmann and Lisinski, we study the theory of the Hahn series field , over a finite field , equipped with the…
A note on existentially t-henselian fields
Sylvy Anscombe
A field is existentially t-henselian if it is has the same existential theory in the first-order language of rings as a field that admits a nontrivial henselian valuation. This pro…
The model theory of perfectoid fields [after Jahnke and Kartas]
Sylvy Anscombe
This text was written to support a Bourbaki seminar given in January 2026 on the subject of the model theory of perfectoid fields, especially on the work of Jahnke and Kartas in th…
Existential fragments of theories of henselian valued fields
Sylvy Anscombe, Arno Fehm
We study fragments of the existential theory of henselian valued fields with parameters. This includes the -fragment in the equicharacteristic or unramified mixed charac…
On Lambda functions in henselian and separably tame valued fields
Sylvy Anscombe
Given a field extension , the ``Lambda closure'' of in is a subextension of that is minimal with respect to inclusion such that is separable.…
Multidimensional asymptotic classes
Sylvy Anscombe, Dugald Macpherson, Charles Steinhorn +1
We develop a general framework (multidimensional asymptotic classes, or m.a.c.s) for handling classes of finite first order structures with a strong uniformity condition on cardina…
Universal-existential theories of fields
Sylvy Anscombe, Arno Fehm
We study various universal-existential fragments of first-order theories of fields, in particular of function fields and of equicharacteristic henselian valued fields. For example…
Interpretations of syntactic fragments of theories of fields
Sylvy Anscombe, Arno Fehm
We set up general machinery to study interpretations of fragments of theories. We then apply this to existential fragments of theories of fields, and especially of henselian valued…
A survey of local-global methods for Hilbert's Tenth Problem
Sylvy Anscombe, Valentijn Karemaker, Zeynep Kisakürek +3
Hilbert's Tenth Problem (H10) for a ring R asks for an algorithm to decide correctly, for each , whether the diophantine equation $f(X_{1},...,X_…
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…
Axiomatizing the existential theory of Fq((t))
Sylvy Anscombe, Philip Dittmann, Arno Fehm
We study the existential theory of equicharacteristic henselian valued fields with a distinguished uniformizer. In particular, assuming a weak consequence of resolution of singular…
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…
Existentially generated subfields of large fields
Sylvy Anscombe
We study subfields of large fields which are generated by infinite existentially definable subsets. We say that such subfields are existentially generated. Let be a large field…
Characterizing diophantine henselian valuation rings and valuation ideals
Sylvy Anscombe, Arno Fehm
We give a characterization, in terms of the residue field, of those henselian valuation rings and those henselian valuation ideals that are diophantine. This characterization gives…
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…
One-dimensional F-definable sets in F((t))
Sylvy Anscombe
In this note we study one-dimensional definable sets in power series fields with perfect residue fields. Using the description of automorphisms given by Schilling, in \cite{S44}, w…
The existential theory of equicharacteristic henselian valued fields
Sylvy Anscombe, Arno Fehm
We study the existential (and parts of the universal-existential) theory of equicharacteristic henselian valued fields. We prove, among other things, an existential Ax-Kochen-Ersho…
Notes on extremal and tame valued fields
Sylvy Anscombe, Franz-Viktor Kuhlmann
We extend the characterization of extremal valued fields given in \cite{[AKP]} to the missing case of valued fields of mixed characteristic with perfect residue field. This leads t…