M-gap conjecture and m-normal theories

We find a small weakly minimal theory with an isolated weakly minimal type of M-rank co and an isolated weakly minimal type of arbitrarily large finite M-rank. These examples lead to the notion of an m-normal theory. We prove the M-gap conjecture for m-normal T. In superstable theories with few countable models we characterize traces of complete types as traces of some formulas. We prove that a 1-based theory with few countable models is m-normal. We investigate generic subgroups of small superstable groups. We compare the notions of independence induced by measure (mu-independence) and category (m-independence).