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Ax-Kochen-Ershov principles for finitely ramified henselian fields
Multi angle
Authors : Dittmann, Philip (Author of the conference)
CIRM (Publisher )
03C60 - Model-theoretic algebra
12L12 - Model theory
CIRM (Publisher )
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Abstract :
Although the class of henselian valued fields of fixed mixed characteristic and fixed finite initial ramification is algebraically well-behaved, it harbours some model-theoretic surprises - for instance, some members of the class fail to be existentially decidable even though their residue field and algebraic part are. I will discuss how to rectify the situation by endowing residue fields with a canonical enrichment of the pure field structure, and how this gives rise to Ax-Kochen-Ershov principles (among other things, describing existential theories and full theories of valued fields in terms of value groups and residue fields). This is joint work with Sylvy Anscombe and Franziska Jahnke.
Keywords : henselian; valued field; finitely ramified; Ax-Kochen-Ershov principle
MSC Codes : Keywords : henselian; valued field; finitely ramified; Ax-Kochen-Ershov principle
03C60 - Model-theoretic algebra
12L12 - Model theory
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 23/06/2023 Conference Date : 02/06/2023 Subseries : Research talks arXiv category : Logic Mathematical Area(s) : Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:00:12 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_06-02_Dittmann_1.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.20051103Cite this video as: Dittmann, Philip (2023). Ax-Kochen-Ershov principles for finitely ramified henselian fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20051103 URI : http://dx.doi.org/10.24350/CIRM.V.20051103 |
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Bibliography
- ANSCOMBE, Sylvy, DITTMANN, Philip, et JAHNKE, Franziska. Ax-Kochen-Ershov principles for finitely ramified henselian fields. arXiv preprint arXiv:2305.12145, 2023. - https://doi.org/10.48550/arXiv.2305.12145
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