  We show how the phenomenon of spontaneous symmetry breakdown is affected by
the presence of a sea of fermions in the system. When its density exceeds a
critical value, the broken symmetry can be restored. We calculate the critical
value and discuss the consequences for three different physical systems: First,
for the standard model of particle physics, where the spontaneous symmetry
breakdown leads nonzero masses of intermediate gauge bosons and fermions. The
symmetry restoration will greatly enhance various processes with dramatic
consequences for the early universe. Second, for the Gell-Mann--L\`evy
$\sigma$-model of nuclear physics, where the symmetry breakdown gives rise to
the nucleon and meson masses. The symmetry restoration may have important
consequences for formation or collapse of stellar cores. Third, for the
superconductive phase of condensed-matter, where the BCS condensate at
low-temperature may be destroyed by a too large electron density.
