Toward classifying unstable theories (Q1923564)

The author tries to classify unstable theories. Theories without the tree property (i.e. simple theories) are investigated; the notion was introduced in the author's paper [Ann. Math. Logic 19, 177-203 (1980; Zbl 0489.03008)]. In Section 1 the author looks at simple theories and it is proved that every simple \(T\) of cardinality \(<\lambda\) has a model in \({\lambda}^{++}\) universal for \({\lambda}^{+}\). In Section 2, the strong order properties are discussed as dividing lines for the classification. A condition for a theory to have few universal models is given.