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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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