8 papers · 1 filter
The generalized continuum hypothesis above a strongly compact cardinal
Zhixing You
We answer a long-standing open question of Woodin by proving that if is a strongly compact cardinal and holds below , then holds.
More notions of forcing add a square
Yair Hayut, Assaf Rinot, Zhixing You
Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed -cc forcing notion for adding . Here,…
A new model for all -sequences are trivial
Assaf Rinot, Zhixing You, Jiachen Yuan
We construct a model in which all -sequences are trivial, yet there exists a -Souslin tree with full vanishing levels. This answers a question of Lambie-Hanson and Rinot, and…
Ketonen's question and other cardinal sins
Assaf Rinot, Zhixing You, Jiachen Yuan
Answering a question of Ketonen from the late 1970's, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtai…
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…
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…
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…
On the cofinality of the least -strongly compact cardinal
Zhixing You, Jiachen Yuan
In this paper, we characterize the possible cofinalities of the least -strongly compact cardinal. We show that, on the one hand, for any regular cardinal, , that carries a $λ…