aka set systm or family of sets

The hypergraph on a ground set X is a subset of the Power set

https://www.wikiwand.com/en/Hypergraph.

There are results in Probabilistic combinatorics about the number of hyperedges of a given size $k$ (assume they all have the same size, such a hypergraph being called $k$-uniform) such that all hypergraphs with less hyperedges than that are guaranteed to be 2-colorable. For hypergraphs with more hyperedges than this number, there exists at least one which is not 2-colorable