  The validity of mode coupling theory (MCT) is restricted by an uncontrolled
factorization approximation of density correlations. The factorization can be
delayed and ultimately avoided, however, by explicitly including higher order
correlations. We explore this approach within a microscopically motivated
schematic model. Analytic tractability allows us to discuss in great detail the
impact of factorization at arbitrary order, including the limit of avoided
factorization. Our results indicate a coherent picture for the capabilities as
well as limitations of MCT. Moreover, including higher order correlations
systematically defers the transition and ultimately restores ergodicity.
Power-law divergence of the relaxation time is then replaced by continuous but
exponential growth.
