On the structure of random hypergraphs

Abstract

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