27 citations · 138 across the 42 of their papers we have counts for
6 papers · 1 filter
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…
Diamond on Kurepa trees
Ziemowit Kostana, Assaf Rinot, Saharon Shelah
We introduce a new weak variation of diamond that is meant to only guess the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by pr…
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 not…
Squares, ultrafilters and forcing axioms
Chris Lambie-Hanson, Assaf Rinot, Jing Zhang
We study relationships between various set theoretic compactness principles, focusing on the interplay between the three families of combinatorial objects or principles mentioned i…