MathDB

Let

\mathcal{H}

be a family of finite subsets of an infinite set

X

such that every finite subset of

X

can be represented as the union of two disjoint sets from

\mathcal{H}

. Prove that for every positive integer

k

there is a subset of

X

that can be represented in at least

k

different ways as the union of two disjoint sets from

\mathcal{H}

. P. Erdos

Problem Statement