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Rainbow Ramsey theorems for colorings establishing negative partition relations

András Hajnal — 2008

Fundamenta Mathematicae

Given a function f, a subset of its domain is a rainbow subset for f if f is one-to-one on it. We start with an old Erdős problem: Assume f is a coloring of the pairs of ω₁ with three colors such that every subset A of ω₁ of size ω₁ contains a pair of each color. Does there exist a rainbow triangle? We investigate rainbow problems and results of this style for colorings of pairs establishing negative "square bracket" relations.

On saturated almost disjoint families

András Hajnal; István Juhász; Lajos Soukup — 1987

Commentationes Mathematicae Universitatis Carolinae

On CCC boolean algebras and partial orders

András Hajnal; István Juhász; Zoltán Szentmiklóssy — 1997

Commentationes Mathematicae Universitatis Carolinae

We partially strengthen a result of Shelah from [Sh] by proving that if $κ = κ^{ω}$ and $P$ is a CCC partial order with e.g. $| P | \leq κ^{+ ω}$ (the $ω^{th}$ successor of $κ$ ) and $| P | \leq 2^{κ}$ then $P$ is $κ$ -linked.

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Rainbow Ramsey theorems for colorings establishing negative partition relations

On saturated almost disjoint families

On CCC boolean algebras and partial orders