Undecidability in some field theories
B Tyrrell - 2023 - ora.ox.ac.uk
This thesis is a study of undecidability in some field theories. Specifically, we are interested
in geometrically oriented problems and have focused our attention in two directions along …
in geometrically oriented problems and have focused our attention in two directions along …
[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 …
Finite Undecidability in Fields II: PAC, PRC and PpC Fields
B Tyrrell - arXiv preprint arXiv:2212.12918, 2022 - arxiv.org
A field $ K $ in a ring language $\mathcal {L} $ is finitely undecidable if $\mbox
{Cons}(\Sigma) $ is undecidable for every nonempty finite $\Sigma\subseteq\mbox …
{Cons}(\Sigma) $ is undecidable for every nonempty finite $\Sigma\subseteq\mbox …
[HTML][HTML] Finite undecidability in PAC and PRC fields
B Tyrrell - Annals of Pure and Applied Logic, 2024 - Elsevier
A field K in a ring language L is finitely undecidable if Cons (Σ) is undecidable for every
nonempty finite Σ⊆ Th (K; L). We adapt arguments originating with Cherlin-van den Dries …
nonempty finite Σ⊆ Th (K; L). We adapt arguments originating with Cherlin-van den Dries …
Definable valuations induced by multiplicative subgroups and NIP fields
K Dupont, A Hasson, S Kuhlmann - Archive for Mathematical Logic, 2019 - Springer
We study the algebraic implications of the non-independence property and variants thereof
(dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are …
(dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are …
Fields with almost small absolute Galois group
A Fehm, F Jahnke - Israel Journal of Mathematics, 2016 - Springer
FIELDS WITH ALMOST SMALL ABSOLUTE GALOIS GROUP Page 1 ISRAEL JOURNAL OF
MATHEMATICS 214 (2016), 193–207 DOI: 10.1007/s11856-016-1356-z FIELDS WITH …
MATHEMATICS 214 (2016), 193–207 DOI: 10.1007/s11856-016-1356-z FIELDS WITH …
[HTML][HTML] Henselianity in the language of rings
S Anscombe, F Jahnke - Annals of Pure and Applied Logic, 2018 - Elsevier
We consider four properties of a field K related to the existence of (definable) henselian
valuations on K and on elementarily equivalent fields and study the implications between …
valuations on K and on elementarily equivalent fields and study the implications between …
Definable valuations on NIP fields
K Dupont - 2015 - kops.uni-konstanz.de
Definable Valuations on NIP Fields Page 1 Definable Valuations on NIP Fields Dissertation
submitted for the degree of Doctor of Natural Science Presented by Katharina Dupont at the …
submitted for the degree of Doctor of Natural Science Presented by Katharina Dupont at the …
[PDF][PDF] Available at http://clok. uclan. ac. uk/22532
S Anscombe, F Jahnke - core.ac.uk
We consider four properties of a field K related to the existence of (definable) henselian
valuations on K and on elementarily equivalent fields and study the implications between …
valuations on K and on elementarily equivalent fields and study the implications between …
Immediately algebraically closed fields
P Sinclair - Illinois Journal of Mathematics, 2021 - projecteuclid.org
We consider two overlapping classes of fields, IAC and VAC, which are defined using
valuation theory but which do not involve a distinguished valuation. Rather, each class is …
valuation theory but which do not involve a distinguished valuation. Rather, each class is …