Problem Statement
Let $m$ be an infinite cardinal and $\kappa$ be the successor cardinal of $2^{\aleph_0}$. Can one colour the countable subsets of $m$ using $\kappa$ many colours so that every $X\subseteq m$ with $\lvert X\rvert=\kappa$ contains subsets of all possible colours?
Categories:
Set Theory Ramsey Theory
Progress
Source: erdosproblems.com/598 | Last verified: January 15, 2026