The tree property on long intervals of regular cardinals
Logic
2025-05-14 v1
Abstract
In this paper we prove that the tree property can hold on regular cardinals in an interval which overlaps a strong limit cardinal. This is a crucial milestone in the long term project, tracing back to a question raised by Foreman and Magidor in the 1980s, of obtaining the tree property at every regular cardinal above the first uncountable cardinal.
Cite
@article{arxiv.2505.08118,
title = {The tree property on long intervals of regular cardinals},
author = {James Cummings and Yair Hayut and Menachem Magidor and Itay Neeman and Dima Sinapova and Spencer Unger},
journal= {arXiv preprint arXiv:2505.08118},
year = {2025}
}