  We try to understand complete types over a somewhat saturated model of a
complete first order theory which is dependent (previously called NIP), by
"decomposition theorems for such types". Our thesis is that the picture of
dependent theory is the combination of the one for stable theories and the one
for the theory of dense linear order or trees (and first we should try to
understand the quite saturated case). As a measure of our progress, we give
several applications considering some test questions; in particular we try to
prove the generic pair conjecture and do it for measurable cardinals.
