A model and its subset: The uncountable case (Q1345008)

This paper continues the study of the relationship between a model and its definable subsets, carried out by the author in earlier papers [J. Symb. Logic 57, 644-658 (1992; Zbl 0774.03015), and ibid. 58, 648-663 (1993; Zbl 0781.03016)]. The methods of these papers are extended to the uncountable case. The main result is the definition of a \(Q\)-isolated type for an arbitrary definable subset. This notion is absolute. For superstable theories the author gives sufficient conditions for the existence of \(Q\)-atomic models and proves results on weak categoricity over a predicate.