The idea behind "admits a classification in the sense of Shelah" is that the class of models of T$T$ in a given cardinal \aleph_\alpha$\aleph_\alpha$ can be described by bounded many numercial invariance (generalizing the situation that a vector space is determined by its dimension). In the case of a countable first-order theory T$T$, if T$T$ admits classification then the number of isomorphism types of models of card \aleph_\alpha$\aleph_\alpha$ is bounded by \beth_{\omega_1}(|\alpha|)$\beth_{\omega_1}(|\alpha|)$. When \alpha$\alpha$ is such that \aleph_\alpha$\aleph_\alpha$ is much bigger than \alpha$\alpha$ then \beth_{\omega_1}(|\alpha|)<< 2^{\aleph_\alpha}$\beth_{\omega_1}(|\alpha|)<< 2^{\aleph_\alpha}$.
Thus I(\lambda,T)=2^\lambda$I(\lambda,T)=2^\lambda$ for all uncountable lambda implies that T$T$ is not classifiable.
