27 citations · 138 across the 42 of their papers we have counts for
52 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 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…
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 uncoun…
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Tanmay Inamdar, Assaf Rinot
It is proved that if there is an -Aronszajn line, then there is one that does not contain an -Countryman line. This solves a problem of Moore and stands in a sh…
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…