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Multi angle Monochromatic sumsets for colourings of $\mathbb{R}$

Auteurs : Soukup, Daniel T. (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : N. Hindman, I. Leader and D. Strauss proved that if $2^{\aleph_0}<\aleph_\omega$ then there is a finite colouring of $\mathbb{R}$ so that no infinite sumset $X+X$ is monochromatic. Now, we prove a consistency result in the other direction: we show that consistently relative to a measurable cardinal for any $c:\mathbb{R}\to r$ with $r$ finite there is an infinite $X\subseteq \mathbb{R}$ so that $c\upharpoonright X+X$ is constant. The goal of this presentation is to discuss the motivation, ideas and difficulties involving this result, as well as the open problems around the topic. Joint work with P. Komjáth, I. Leader, P. Russell, S. Shelah and Z. Vidnyánszky.

    Codes MSC :
    03E02 - Partition relations
    03E35 - Consistency and independence results
    05D10 - Ramsey theory

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 12/10/2017
      Date de captation : 11/10/2017
      Collection : Research talks
      Format : MP4
      Durée : 00:31:43
      Domaine : Logic and Foundations ; Combinatorics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2017-10-11_Soukup.mp4

    Informations sur la rencontre

    Nom du congrès : 14th International workshop in set theory / XIVe Atelier international de théorie des ensembles
    Organisteurs Congrès : Dzamonja, Mirna ; Magidor, Menachem ; Velickovic, Boban ; Woodin, W. Hugh
    Dates : 09/10/2017 - 13/10/2017
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1606.html

    Citation Data

    DOI : 10.24350/CIRM.V.19227703
    Cite this video as: Soukup, Daniel T. (2017). Monochromatic sumsets for colourings of $\mathbb{R}$. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19227703
    URI : http://dx.doi.org/10.24350/CIRM.V.19227703

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