4 papers · 1 filter
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…
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…
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…
A Shelah group in ZFC
Márk Poór, Assaf Rinot
In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group $G…