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Transfer of decidability for existential theories of (valued) fields
Multi angle
Authors : Anscombe, Sylvy (Author of the conference)
CIRM (Publisher )
03C60 - Model-theoretic algebra
11D88 - $p$-adic and power series fields
12L05 - Decidability, See also {03B25}
CIRM (Publisher )
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Abstract :
In previous work with Fehm we found that the existential theory of an equicharacteristic henselian valued field is axiomatised using the existential theory of its residue field. From this we deduced a transfer of decidability: for a complete theory $T$ of residue fields, the existential consequences of $T$ are decidable if and only if the existential consequences of the theory $H(T)$ are decidable, where $H(T)$ is 'equicharacteristic, henselian, and residue field models $T^{\prime}$. In more recent work with Dittmann and Fehm we considered a similar problem in which $H(T)$ is expanded to a theory that distinguishes a uniformizer, using an additional constant symbol. In this case Denef and Schoutens gave a transfer of existential decidability conditional on Resolution of Singularities. We introduce a consequence of Resolution and prove that it implies a similar transfer of existential decidability.In this talk I'll explain these results and describe ongoing work with Fehm in which we broaden the above setting to obtain versions of these transfer results that allow incomplete theories $T$. Consequently we find several existential theories Turing equivalent to the existential theory of $\mathbb{Q}$, including the existential theory of large fields.
Keywords : henselian; existential theory; decidable
MSC Codes : Keywords : henselian; existential theory; decidable
03C60 - Model-theoretic algebra
11D88 - $p$-adic and power series fields
12L05 - Decidability, See also {03B25}
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/06/2023 Conference Date : 01/06/2023 Subseries : Research talks arXiv category : Logic Mathematical Area(s) : Algebra ; Analysis and its Applications ; Dynamical Systems & ODE ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:02:55 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-01_Anscombe.mp4 
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Information on the Event
Event Title : Model theory of valued fields / Théorie des modèles des corps valuésEvent Organizers : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain Dates : 29/05/2023 - 02/06/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2761.html
Citation Data
DOI : 10.24350/CIRM.V.20050203Cite this video as: Anscombe, Sylvy (2023). Transfer of decidability for existential theories of (valued) fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20050203 URI : http://dx.doi.org/10.24350/CIRM.V.20050203 |
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Bibliography
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