The tree property on long intervals of regular cardinals
James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova, Spencer Unger
TL;DR
This paper demonstrates that the tree property can be established on a range of regular cardinals overlapping a strong limit cardinal, advancing the goal of having the property at all regular cardinals above the first uncountable.
Contribution
It proves the tree property can hold on an interval of regular cardinals overlapping a strong limit, addressing a longstanding open question in set theory.
Findings
Tree property holds on an interval of regular cardinals overlapping a strong limit.
Progress towards the goal of tree property at all regular cardinals above .
Advances the understanding of combinatorial properties of large cardinals.
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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