Erdős–Rado sunflower conjecture

Let $[n]:=\{1,2,\ldots,n\}$. For $k\geq 3$, a family $\mathcal{F}$ of subsets of $[n]$ is $k$-sunflower free if it contains no $k$ pairwise distinct sets whose pairwise intersections are all equal. In the uniform setting, every member of $\mathcal{F}$ has size $m$. Erdős–Rado sunflower conjecture. For $k\geq 3$, let $\mathcal{F}$ be a $k$-sunflower free family of $m$-subsets of $[n]$. Then

$$|\mathcal{F}|\leq \mu^m$$

for a constant $\mu$ depending only on $k$. This is the uniform sunflower conjecture for set systems; the paper presents it as the conjecture introduced by Erdős and Rado, while the supplied text gives no resolution status.