[en] An equation of state for neutron matter which includes relativistic pion exchange is used to calculate neutron star masses and moments of inertia. The equation of state sets a reasonable lower bound on the softness of cold superdense matter, and leads to a maximum equilibrium neutron star mass of 0.52 M/sub sun/. Processes which could affect our conclusions, such as hyperionization, nonnormal ground states, solidification and local anisotropy are discussed