  Within the mode-coupling theory for the evolution of structural relaxation,
the A_4 glass-transition singularities are identified for systems of particles
interacting with a hard-sphere repulsion complemented by different short-ranged
potentials: Baxter's singular potential regularized by a large-wave-vector
cutoff, a model for the Asakura-Oosawa depletion attraction, a triangular
potential, a Yukawa attraction, and a square-well potential. The regular
potentials yield critical packing fractions, critical Debye-Waller factors and
critical amplitudes very close to each other. The elastic moduli and the
particle's localization lengths for corresponding states of the Yukawa system
and the square-well system may differ by up to 20% and 10%, respectively.
