Hereditary properties of hypergraphs

A hereditary property P(k) is a class of k-graphs closed under isomorphism and taking induced sub-hypergraphs. Let denote those k-graphs of P(k) on vertex set {1,…,n}. We prove an asymptotic formula for in terms of a Turán-type function concerning forbidden induced sub-hypergraphs. This result complements several existing theorems for hereditary and monotone graph and hypergraph properties.