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 …
Existential first-order definitions and quadratic forms
N Daans - 2022 - repository.uantwerpen.be
Answering a famous question of David Hilbert, it was shown by Davis, Putnam, Robinson
and Matiyasevich in 1970 that there can never be an algorithm which can decide whether or …
and Matiyasevich in 1970 that there can never be an algorithm which can decide whether or …
Ordered fields dense in their real closure and definable convex valuations
LS Krapp, S Kuhlmann, G Lehéricy - Forum Mathematicum, 2021 - degruyter.com
In this paper, we undertake a systematic model-and valuation-theoretic study of the class of
ordered fields which are dense in their real closure. We apply this study to determine …
ordered fields which are dense in their real closure. We apply this study to determine …
Definability of henselian valuations by conditions on the value group
LS Krapp, S Kuhlmann, M Link - The Journal of Symbolic Logic, 2023 - cambridge.org
Given a Henselian valuation, we study its definability (with and without parameters) by
examining conditions on the value group. We show that any Henselian valuation whose …
examining conditions on the value group. We show that any Henselian valuation whose …
[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 …
Definable henselian valuations on dp-minimal real fields
LS Krapp, S Kuhlmann, L Vogel - arXiv preprint arXiv:2410.10344, 2024 - arxiv.org
We give an explicit algebraic characterisation of all definable henselian valuations on a dp-
minimal real field. Additionally we characterise all dp-minimal real fields that admit a …
minimal real field. Additionally we characterise all dp-minimal real fields that admit a …
Definable Henselian valuations in positive residue characteristic
M Ketelsen, S Ramello, P Szewczyk - arXiv preprint arXiv:2401.06884, 2024 - arxiv.org
We study the question of $\mathcal {L} _ {\mathrm {ring}} $-definability of non-trivial
henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we …
henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we …
Definable valuations on ordered fields
P Dittmann, F Jahnke, LS Krapp, S Kuhlmann - Model Theory, 2023 - msp.org
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, one can …
the distinguished subclass of henselian valuations. In the setting of ordered fields, one can …
Truncation in differential Hahn fields
S Camacho - arXiv preprint arXiv:1806.05309, 2018 - arxiv.org
Being closed under truncation for subsets of generalized series fields is a robust property in
the sense that it is preserved under various algebraic and transcendental extension …
the sense that it is preserved under various algebraic and transcendental extension …