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math.LO2026
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,…
math.LO2025
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…
math.LO2025
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, an…