Upper Bounds on Tur\'an Densities via Extremal Set Theory

We exhibit, in a systematic way, connections between hypergraph Tur\'an problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for which the upper bounds on their Tur\'an densities reduce to classical problems in extremal set theory, including the Erd\H{o}s--Ko--Rado theorem, $L$-intersecting families, and the Erd\H{o}s matching problem.