Dependent theories and the generic pair conjecture
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2007
 arXiv:
 arXiv:math/0702292
 Bibcode:
 2007math......2292S
 Keywords:

 Mathematics  Logic;
 03C45;
 03C55