Bicolour painting of the Descartes products - Zelenyuk, E. G.; Malykhin, V. I. (Ukrains’kyi Matematychnyi Zhurnal, 1990)
We shall color the Cartesian product $ω ´ ω_1$ with two colors. Can an infinite subset $A\subset ω$ and an uncountable subset $B\subset ω_1$ be found such that the product $A´B$ can be one-colored? This problem proves to be unsolvable in $ZFC$.