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arXiv · 2505.08118

The tree property on long intervals of regular cardinals

James Cummings·Yair Hayut·Menachem Magidor·Itay Neeman·Dima Sinapova·Spencer Unger
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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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James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova, Spencer Unger. 2025-05-12. The tree property on long intervals of regular cardinals. https://arxiv.org/abs/2505.08118

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