  A proof of Goldstone's theorem is given for the case in which global chiral
symmetry is dynamically broken. The proof highlights a needed consistency
between the exact Schwinger--Dyson equation for the fermion propagator and the
exact Bethe--Salpeter equation for fermion--antifermion bound states. A
criterion, based on the Cornwall, Jackiw and Tomboulis effective action for
composite operators, is provided for maintaining the consistency when the
equations are modified by approximations. For gauge theories in which partial
conservation of the axial current (PCAC) should hold, a constraint on the
approximations to the fermion--gauge boson vertex function is discussed, and a
vertex model is given which satisfies both the PCAC constraint and the vector
Ward--Takahashi identity.
