Hajnal, András Rainbow Ramsey theorems for colorings establishing negative partition relations. (English) Zbl 1142.03027 Fundam. Math. 198, No. 3, 255-262 (2008). Summary: 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 \(\omega_1\) with three colors such that every subset \(A\) of \(\omega_1\) of size \(\omega_1\) 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. Cited in 2 Documents MSC: 03E02 Partition relations 03E05 Other combinatorial set theory Keywords:partition relation; rainbow subset; coloring PDFBibTeX XMLCite \textit{A. Hajnal}, Fundam. Math. 198, No. 3, 255--262 (2008; Zbl 1142.03027) Full Text: DOI