Thomas, S.2019-02-072019-02-071996-08-050168-0072http://hdl.handle.net/11693/49063For each k ⩾ 1, let Γk be the countable universal homogeneous k-hypergraph. In this paper, we shall classify the closed permutation groups G such that Aut(Γk) ⩽ G ⩽ Sym(Γk). In particular, we shall show that there exist only finitely many such groups G for each k ⩾ 1. We shall also show that each of the associated reducts of Γk is homogeneous with respect to a finite relational language.EnglishArticle10.1016/0168-0072(95)00061-51873-2461