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math.LO2023
The vanishing levels of a tree
Assaf Rinot, Shira Yadai, Zhixing You
We initiate the study of the spectrum of sets that can be realized as the vanishing levels of a normal -tree . The latter is an invariant in the sense that…
math.LO2023
Full Souslin trees at small cardinals
Assaf Rinot, Shira Yadai, Zhixing You
A -tree is said to be full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full -Souslin tree may consistently exist. Shelah gave a…
math.LO2023
How far is almost strong compactness from strong compactness
Zhixing You, Jiachen Yuan
Bagaria and Magidor introduced the notion of almost strong compactness, which is very close to the notion of strong compactness. Boney and Brooke-Taylor asked whether the least alm…