On Nonstructure of Elementary Submodels of an Unsuperstable Homogeneous Structure

In the first part of this paper we let M be a stable homogeneous model and we prove a nonstructure theorem for the class of all elementary submodels of M, assuming that M is ‘unsuperstable’ and has Skolem functions. In the second part we assume that M is an unstable homogeneous model of large cardinality and we prove a nonstructure theorem for the class of all elementary submodels of M.