6 papers
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,…
The power of trees
Ari Meir Brodsky, Assaf Rinot, Shira Yadai
We give two consistent constructions of trees whose finite power is sharply different from : 1. An -tree whose interval topology is perfectly…
A model for global compactness
Sittinon Jirattikansakul, Inbar Oren, Assaf Rinot
In a classical paper by Ben-David and Magidor, a model of set theory was exhibited in which carries a uniform ultrafilter that is -indecomposable for every unco…
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…
Proxy principles in combinatorial set theory
Ari Meir Brodsky, Assaf Rinot, Shira Yadai
The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper, as new foundations for the construction of -Souslin trees in a uniform way that does no…
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…