English

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.

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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}
}