XVIII International Workshop in Set Theory / XVIII Atelier International de Théorie des Ensembles

Collection XVIII International Workshop in Set Theory / XVIII Atelier International de Théorie des Ensembles

Organizer(s) Mueller, Sandra ; Nguyen Van The, Lionel ; Velickovic, Boban ; Viale, Matteo

Date(s) 03/11/2025 - 07/11/2025

linked URL https://conferences.cirm-math.fr/3332.html

00:00:00 / 00:00:00

3 5

The tree property on long intervals

By Dima Sinapova

An old project in set theory is to force the tree property at every regular cardinal above $\omega_1$. We present the current state of the art towards it, by obtaining the tree property at every regular in the interval $\left[\omega_2, \aleph_{\omega^2+3}\right]$. This is the first construction where the tree property holds across a singular strong limit. This is joint work with Cummings, Hayut, Magidor, Neeman, and Unger.

Information about the video

Date of recording 04/11/2025
Date of publication 25/11/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20402203
Cite this video Sinapova, Dima (04/11/2025). The tree property on long intervals. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20402203
URL https://dx.doi.org/10.24350/CIRM.V.20402203

Domain(s)

Logic

Bibliography

CUMMINGS, James, HAYUT, Yair, MAGIDOR, Menachem, et al. The tree property on long intervals of regular cardinals. arXiv preprint arXiv:2505.08118, 2025. - https://doi.org/10.48550/arXiv.2505.08118

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