On the divisibility of homogeneous hypergraphs
Let \(k\geq 3\) and \(T\) be a family of \(k\)-hypergraphs in which every 3- element subset of the ground set is covered by a member of \(T\). Then the countable homogeneous \(T\)-free hypergraph is indivisible, i.e., has the vertex Ramsey property. A weaker property is described if the covering of pairs is satisfied. Other properties as well as a counterexample are also given.
scientific article; zbMATH DE number 617053