Toward Classifying Unstable Theories

We prove a consistency results saying, that for a simple (first order) theory, it is easier to have a universal model in some cardinalities, than for the theory of linear order. We define additional properties of first order theories, the n-strong order property (SOPn in short). The main result is that a first order theory with the 4-strong order property behaves like linear orders concerning existence of universal models.