= Independent family of sets
{title2=$\bigcap_{j=1}^m A_j^{\varepsilon_j}\ne\varnothing$}
= Independent family of subsets
{synonym}
A family of <subsets> of $X$ is independent when every finite choice of distinct members and their complements has nonempty <intersection>. Write $A^1=A$ and $A^0=X\setminus A$ in the displayed condition. Every assignment of zero or one to the family then gives a collection with the <finite intersection property>, which can be extended to an <ultrafilter>.
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