  In this article, we use an electromagnetic gauge-free framework to establish
the existence of small-data global solutions to the Maxwell-Born-Infeld (MBI)
system on the Minkowski space background in 1 + 3 dimensions. Because the
nonlinearities in the system satisfy a version of the null condition, we are
also able to show that these solutions decay at exactly the same rates as
solutions to the linear Maxwell-Maxwell system. In addition, we show that on
any Lorentzian manifold, the MBI system is hyperbolic in the interior of the
field-strength regime in which its Lagrangian is real-valued.
