The existential theory of equicharacteristic henselian valued fields
S Anscombe, A Fehm - Algebra & Number Theory, 2016 - msp.org
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–Ershov …
henselian valued fields. We prove, among other things, an existential Ax–Kochen–Ershov …
Axiomatizing the existential theory of 𝔽q ((t))
S Anscombe, P Dittmann, A Fehm - Algebra & Number Theory, 2023 - msp.org
We study the existential theory of equicharacteristic henselian valued fields with a
distinguished uniformizer. In particular, assuming a weak consequence of resolution of …
distinguished uniformizer. In particular, assuming a weak consequence of resolution of …
Universal-existential theories of fields
S Anscombe, A Fehm - arXiv preprint arXiv:2405.12771, 2024 - arxiv.org
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 we discuss …
of function fields and of equicharacteristic henselian valued fields. For example we discuss …
Interpretations of syntactic fragments of theories of fields
S Anscombe, A Fehm - arXiv preprint arXiv:2312.17616, 2023 - arxiv.org
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 fields. As …
this to existential fragments of theories of fields, and especially of henselian valued fields. As …
Existential rank and essential dimension of diophantine sets
arXiv:2102.06941v3 [math.NT] 18 Oct 2021 Page 1 arXiv:2102.06941v3 [math.NT] 18 Oct 2021
EXISTENTIAL RANK AND ESSENTIAL DIMENSION OF DIOPHANTINE SETS NICOLAS …
EXISTENTIAL RANK AND ESSENTIAL DIMENSION OF DIOPHANTINE SETS NICOLAS …
[图书][B] Recent progress on definability of Henselian valuations
A Fehm, F Jahnke - 2017 - books.google.com
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. We …
J. Robinson, most of the results in this area were proven during the last few years. We …
A model-theoretic approach to the arithmetic of global fields
P Dittmann - 2018 - ora.ox.ac.uk
This thesis assembles some new results in the field arithmetic of various classes of fields,
including global fields, models of the common first-order theory of algebraic extensions of …
including global fields, models of the common first-order theory of algebraic extensions of …
Growing Spines Ad Infinitum
B Boissonneau, A De Mase, F Jahnke… - arXiv preprint arXiv …, 2025 - arxiv.org
We show that every non-trivial ordered abelian group $ G $ is augmentable by infinite
elements, ie, we have $ G\preccurlyeq H\oplus G $ for some non-trivial ordered abelian …
elements, ie, we have $ G\preccurlyeq H\oplus G $ for some non-trivial ordered abelian …
[PDF][PDF] On the existential theory of the completions of a global field
P Dittmann, A Fehm - arXiv preprint arXiv:2401.11930, 2024 - arxiv.org
arXiv:2401.11930v1 [math.LO] 22 Jan 2024 Page 1 arXiv:2401.11930v1 [math.LO] 22 Jan 2024
ON THE EXISTENTIAL THEORY OF THE COMPLETIONS OF A GLOBAL FIELD PHILIP …
ON THE EXISTENTIAL THEORY OF THE COMPLETIONS OF A GLOBAL FIELD PHILIP …
Denseness results in the theory of algebraic fields
S Anscombe, P Dittmann, A Fehm - Annals of Pure and Applied Logic, 2021 - Elsevier
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