Simple groups and the number of countable models

Let T be a complete, superstable theory with fewer than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${2^{\aleph_{0}}}$$\end{document} countable models. Assuming that generic types of infinite, simple groups definable in Teq are sufficiently non-isolated we prove that ωω is the strict upper bound for the Lascar rank of T.