Simple groups and the number of countable models

Abstract

Let $T$ be a complete, superstable theory with fewer than $2^{{\aleph }_0}$ countable models. Assuming that generic types of infinite, simple groups definable in $T^{eq}$ are sufficiently non-isolated we prove that ${\omega }^{\omega }$ is the strict upper bound for the Lascar rank of $T$.

arXiv commentSubmitted to Achive for Mathematical Logic