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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-3-4,
author = {Andr\'as Hajnal},
title = {Rainbow Ramsey theorems for colorings establishing negative partition relations},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {255-262},
zbl = {1142.03027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-3-4}
}
András Hajnal. Rainbow Ramsey theorems for colorings establishing negative partition relations. Fundamenta Mathematicae, Tome 201 (2008) pp. 255-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-3-4/