### Dependent theories and the generic pair conjecture

by Shelah. [Sh:900]

Communications in Contemporary Math, 2015

On the one hand we try to understand complete types over
somewhat saturated model of a complete first order theory which is
dependent, 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). On the other hand 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. The order of the sections is by their
conceptions, so there are some repetitions.

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