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Given a finite poset $\mathcal P$, we say that a family $\mathcal F$ of subsets of $[n]$ is $\mathcal P$-saturated if $\mathcal F$ does not contain an induced copy of $\mathcal P$, but adding any other set to $\mathcal F$ creates an induced copy of $\mathcal P$.
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A. Freschi, S. Piga, M. Sharifzadeh, and A. Treglown, The induced saturation problem for posets , ar χ \chi iv: 2207.03974 (2022)
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