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H 1 Reflection of stationary sets and the tree property at $\aleph_{\omega^2+1}$

Auteurs : Fontanella, Laura (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The combinatorics of successors of singular cardinals presents a number of interesting open problems. We discuss the interactions at successors of singular cardinals of two strong combinatorial properties, the stationary set reflection and the tree property. Assuming the consistency of infinitely many supercompact cardinals, we force a model in which both the stationary set reflection and the tree property hold at $\aleph_{\omega^2+1}$. Moreover, we prove that the two principles are independent at this cardinal, indeed assuming the consistency of infinitely many supercompact cardinals it is possible to force a model in which the stationary set reflection holds, but the tree property fails at $\aleph_{\omega^2+1}$. This is a joint work with Menachem Magidor.
    Keywords : forcing - large cardinals - successors of singular cardinals - stationary reflection - tree property

    Codes MSC :
    03E05 - Combinatorial set theory (logic)
    03E35 - Consistency and independence results
    03E55 - Large cardinals

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 28/10/14
      Date de captation : 30/09/14
      Collection : Logic and Foundations
      Sous collection : Research talks
      Format : quicktime ; audio/x-aac
      Domaine : Logic and Foundations
      Durée : 00:32:08
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-09-30_Fontanella.mp4

    Informations sur la rencontre

    Nom de la rencontre : 13th International workshop in set theory / 13ème Atelier international de théorie des ensembles
    Organisateurs de la rencontre : Louveau, Alain ; Magidor, Menachem ; Velickovic, Boban
    Dates : 29/09/14 - 03/10/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18605703
    Cite this video as: Fontanella, Laura (2014). Reflection of stationary sets and the tree property at $\aleph_{\omega^2+1}$. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18605703
    URI : http://dx.doi.org/10.24350/CIRM.V.18605703


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