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math.LO2025
The tree property on long intervals of regular cardinals
James Cummings, Yair Hayut, Menachem Magidor +3
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 proj…
math.LO2025
Isomorphism Classes of Generating Sets
Tom Benhamou, James Cummings, Gabriel Goldberg +2
We introduce a new class of ultrafilters which generalizes the well-known class of simple -point ultrafilters. We prove that for any well-founded -directed partial order $\ma…
math.LO2025
On a problem of Erdos and Hajnal
Shimon Garti, Yair Hayut, Saharon Shelah
We address a question of Erdős and Hajnal about the ordinary partition relation . For , assuming $2^λ=λ…