  We show that facilitated spin models of cooperative dynamics introduced by
Fredrickson and Andersen display on Bethe lattices a glassy behaviour similar
to the one predicted by the mode-coupling theory of supercooled liquids and the
dynamical theory of mean-field disordered systems. At low temperature such
cooperative models show a two-step relaxation and their equilibration time
diverges at a finite temperature according to a power-law. The geometric nature
of the dynamical arrest corresponds to a bootstrap percolation process which
leads to a phase space organization similar to the one of mean-field disordered
systems. The relaxation dynamics after a subcritical quench exhibits aging and
converges asymptotically to the threshold states that appear at the bootstrap
percolation transition.
