Bicolour painting of the Descartes products

• Date: 1990
• Main Authors: Zelenyuk, E. G., Malykhin, V. I., Зеленюк, Е. Г., Малыхин, В. И.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1990
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8852
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We shall color the Cartesian product $\omega ´ \omega_1$ with two colors. Can an infinite subset $A\subset \omega$ and an uncountable subset $B\subset \omega_1$ be found such that the product $A´B$ can be one-colored? This problem proves to be unsolvable in $ZFC$.