Collection XVI International Luminy Workshop in Set Theory / XVI Atelier international de théorie des ensembles

Organisateur(s) Fischer, Vera ; Velickovic, Boban ; Viale, Matteo

Date(s) 13/09/2021 - 17/09/2021

URL associée https://conferences.cirm-math.fr/2370.html

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Universal ${ \aleph }_{2}$-Aronszajn trees

We report on a joint work in progress with Rahman Mohammadpour in which we study the problem of the possible existence of a universal tree under weak embeddings in the classes of $\aleph_{2}$-Aronszajn and wide $\aleph_{2}$-Aronszajn trees. This problem is more complex than previously thought, in particular it seems not to be resolved under ShFA $+$ CH using the technology of weakly Lipshitz trees. We show that under CH, for a given $\aleph_{2}$-Aronszajn tree $\mathrm{T}$ without a weak ascent path, there is an $\aleph_{2^{-\mathrm{C}\mathrm{C}}}$ countably closed forcing forcing which specialises $\mathrm{T}$ and adds an $\aleph_{2}$-Aronszajn tree which does not embed into T. One cannot however apply the ShFA to this forcing.

Informations sur la vidéo

Date de captation 16/09/2021
Date de publication 04/10/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19809103
Citer cette vidéo Dzamonja, Mirna (16/09/2021). Universal ${ \aleph }_{2}$-Aronszajn trees. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19809103
URL https://dx.doi.org/10.24350/CIRM.V.19809103

Domaine(s)

Logique

Bibliographie

Džamonja, Mirna, and Saharon Shelah. "On wide Aronszajn trees in the presence of MA." The Journal of Symbolic Logic (2020): 1-18. - https://doi.org/10.1017/jsl.2020.42