Elekes, G.; Hajnal, András; Komjáth, P. Partition theorems for the power set. (English) Zbl 0785.05085 Halász, G. (ed.) et al., Sets, graphs and numbers. A birthday salute to Vera T. Sós and András Hajnal. Amsterdam: North-Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 60, 211-217 (1992). Summary: The power set of any set can be colored by countably many colors such that there do not exist infinitely many disjoint subsets with all finite subunions getting the same color. Two colors suffice for the case of infinite subunions or when uncountably many subsets are required. If GCH holds, \(\text{cf}(\lambda)>\kappa\), and the power set of a set of size \(\lambda\) is \(\kappa\)-colored, then there exist \(\lambda\) disjoint monochromatic sets such that their union also gets the same color.For the entire collection see [Zbl 0925.05001]. Cited in 3 Documents MSC: 05D10 Ramsey theory Keywords:partition theorems; power set PDFBibTeX XMLCite \textit{G. Elekes} et al., in: Sets, graphs and numbers. A birthday salute to Vera T. Sós and András Hajnal. Amsterdam: North-Holland Publishing Company. 211--217 (1992; Zbl 0785.05085)