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Beautiful pairs revisited

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Authors : Ye, Jinhe (Author of the conference)
CIRM (Publisher )

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Abstract : We extend the notion of beautiful pairs by Poizat to unstable theories via definable types, with a specific interest in such pairs of valued fields. In particular, we establish an analogue of Ax-Kochen-Ershov principles in for certain pairs of valued fields. In the specific case of ACVF, we classify all such pairs and deduce the strict pro-definability of various spaces of definable types, such as the stable completion introduced by Hrushovski-Loeser and a model theoretic analogue of the Huber analytification of an algebraic variety. This is joint with Pablo Cubides Kovacsics and Martin Hils.

Keywords : beautiful pairs; valued fields; pro-definability; Ax-Kochen-Ershov principle

MSC Codes :
03C10 - Quantifier elimination and related topics
03C45 - Classification theory, stability and related concepts [See also 03C48]
03C64 - Model theory of ordered structures; o-minimality
12J10 - Valued fields
12L12 - Model theory

    Information on the Video

    Film maker : Petit, Jean
    Language : English
    Available date : 23/06/2023
    Conference Date : 30/05/2023
    Subseries : Research talks
    arXiv category : Logic
    Mathematical Area(s) : Logic and Foundations
    Format : MP4 (.mp4) - HD
    Video Time : 00:56:16
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2023_05-30_Ye_1.mp4

Information on the Event

Event Title : Model theory of valued fields / Théorie des modèles des corps valués
Event 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.20053903
Cite this video as: Ye, Jinhe (2023). Beautiful pairs revisited. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20053903
URI : http://dx.doi.org/10.24350/CIRM.V.20053903

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