3 papers
math.LO2026
Compactness phenomena in HOD and the Optimality of Magidor's Covering theorem
Tom Benhamou, James Cummings, Yair Hayut +2
We continue the study of compactness phenomena between the set-theoretic universe and initiated by Goldberg--Poveda \cite{GolPov}. We focus on compactness phenomena…
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…