Dependent first order theories, continued

by Shelah. [Sh:783]
Israel J Math, 2009
A dependent theory is a (first order complete theory) T which does not have the independence property. A major result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being dependent. Another one justifies the cofinality restriction in the theorem (from a previous work) saying that pairwise perpendicular indiscernible sequences, can have arbitrary dual-cofinalities in some models containing them. We introduce ``strongly dependent'' and look at definable groups; and also at dividing, forking and relatives.

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