Let $X$ be an infinite set, and let $(A_n)_{n\in\omega}$ be a collection of subsets of $X$ with the following properties:

- $|A_m\cap A_n| \leq 1$ for $m\neq n\in \omega$, and
- $|A_n|=\aleph_0$ for all $n\in \omega$.

We consider the following statement:

(EFL$_\omega$:) There is $f:X\to \omega$ such that for all $n\in\omega$ the restriction $f|_{A_n}:A_n\to\omega$ is a bijection.

**Questions.** Is (EFL$_\omega$) true? Or does (EFL$_\omega$) imply the original Erdös-Faber-Lovasz conjecture?