M-gap conjecture and m-normal theories

We find a small weakly minimal theory with an isolated weakly minimal type ofM-rank ∞ and an isolated weakly minimal type of arbitrarily large finiteM-rank. These examples lead to the notion of an m-normal theory. We prove theM-gap conjecture for m-normalT. 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 (μ-independence) and category (m-independence). Research supported by KBN grant 2 P03A 006 09.