1-based theories — the main gap fora-models

We prove the “Main Gap” for the class ofa-models (sufficiently saturated models) of an arbitrary stable 1-based theoryT. We (i) prove a strong structure theorem fora-models, assuming NDOP, and (ii) roughly compute the number ofa-models ofT in any given cardinality.The analysis uses heavily group existence theorems in 1-based theories.