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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 )

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, BobanDates : 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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