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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