If $H=(V,E)$ is a hypergraph such that $V\neq\varnothing\neq E$ and $|e| > 1$ for all $e\in E$, and $\kappa\neq\varnothing$ is a cardinal, we say that a map $c:V\to\kappa$ is a *coloring* if the restriction $c\restriction_e: e\to \kappa$ is non-constant for each $e\in E$. We denote by $\chi(H)$ the smallest cardinal $\kappa$ such that there is a coloring $c:V \to \kappa$.

Assume the Axiom of Choice. If ${\cal A, B}$ are infinite maximal almost disjoint families on $\omega$, do we necessarily have $\chi((\omega, {\cal A}))=\chi((\omega,{\cal B}))$?

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