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H 1 O-minimalism: the first-order properties of o-minimality

Auteurs : Schoutens, Hans (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : O-minimalism is the first-order theory of o-minimal structures, an important class of models of which are the ultraproducts of o-minimal structures. A complete axiomatization of o-minimalism is not known, but many results are already provable in the weaker theory DCTC given by definable completeness and type completeness (a small extension of local o-minimality). In DCTC, we can already prove how many results from o-minimality (dimension theory, monotonicity, Hardy structures) carry over to this larger setting upon replacing ‘finite’ by ‘discrete, closed and bounded’. However, even then cell decomposition might fail, giving rise to a related notion of tame structures. Some new invariants also come into play: the Grothendieck ring is no longer trivial and the definable, discrete subsets form a totally ordered structure induced by an ultraproduct version of the Euler characteristic. To develop this theory, we also need another first-order property, the Discrete Pigeonhole Principle, which I cannot yet prove from DCTC. Using this, we can formulate a criterion for when an ultraproduct of o-minimal structures is again o-minimal.

    Codes MSC :
    03C64 - Model theory of ordered structures; o-minimality

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 12/11/15
      Date de captation : 13/10/15
      Collection : Research talks ; Algebra ; Logic and Foundations
      Format : MP4
      Durée : 00:32:10
      Domaine : Algebra ; Logic and Foundations
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-10-15_Schoutens.mp4

    Informations sur la rencontre

    Nom de la rencontre : Ordered algebraic structures and related topics / Structures algébriques ordonnées et leurs interactions
    Organisateurs de la rencontre : Broglia, Fabrizio ; Delon, Francoise ; Dickmann, Max ; Gondard, Danielle
    Dates : 12/10/15 - 16/10/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1155.html

    Citation Data

    DOI : 10.24350/CIRM.V.18864503
    Cite this video as: Schoutens, Hans (2015). O-minimalism: the first-order properties of o-minimality. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18864503
    URI : http://dx.doi.org/10.24350/CIRM.V.18864503


    Bibliographie

    1. Schoutens, H. (2014). O-minimalism. The Journal of Symbolic Logic, 79(2), 355-409 - http://dx.doi.org/10.1017/jsl.2013.14

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