27 citations · 138 across the 42 of their papers we have counts for
7 papers · 2 filters
Was Ulam right? I: Basic theory and subnormal ideals
Tanmay Inamdar, Assaf Rinot
We introduce various colouring principles which generalise the so-called "onto mapping principle" of Sierpinski to larger cardinals and general ideals. We prove that these principl…
Knaster and friends III: Subadditive colorings
Chris Lambie-Hanson, Assaf Rinot
We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals ,…
Strongest transformations
Assaf Rinot, Jing Zhang
We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC,…
On the ideal
Assaf Rinot
Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal , from which we confirm that -Souslin trees ex…
A guessing principle from a Souslin tree, with applications to topology
Assaf Rinot, Roy Shalev
We introduce a new combinatorial principle which we call . This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointne…
Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Menachem Kojman, Assaf Rinot, Juris Steprans
The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of real…