5 citations · 14 across the 26 of their papers we have counts for
28 papers
Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems
Menachem Kojman, Assaf Rinot, Juris Steprans
In this series of papers we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong coloring…
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…
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
Menachem Kojman, Assaf Rinot, Juris Steprans
In this series of papers, we advance Ramsey theory of colorings over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and chain conditions of…
Strong colorings over partitions
William Chen-Mertens, Menachem Kojman, Juris Steprans
A strong coloring on a cardinal is a function such that for every of full size , every color is attained by . The…
On the arithmetic of density
Menachem Kojman
The -density of a cardinal is the least cardinality of a dense collection of -subsets of and is denoted by . The Singular Density Hypothesis (SDH…
Splitting families of sets in ZFC
Menachem Kojman
Miller's 1937 splitting theorem was proved for pairs of cardinals $(\n,ρ)$ in which is finite and is infinite. An extension of Miller's theorem is proved here in ZFC for pa…