On the structure of random hypergraphs

Abstract

Let Hn be a countable random n-uniform hypergraph for n > 2, and P(Hn) = {f [Hn] : f : Hn → Hn is an embedding}. We prove that a linear order L is isomorphic to the maximal chain in the partial order P(Hn)∪{∅}, ⊂ if and only if L is isomorphic to the order type of a compact set of reals whose minimal element is nonisolated.