  It has recently been shown within a formal axiomatic framework using a
definition of four-momentum based on the St\"uckelberg-Feynman-Sudarshan-Recami
"switching principle" that Einstein's relativistic dynamics is logically
consistent with the existence of interacting faster-than-light inertial
particles. Our results here show, using only basic natural assumptions on
dynamics, that this definition is the only possible way to get a consistent
theory of such particles moving within the geometry of Minkowskian spacetime.
We present a strictly formal proof from a streamlined axiom system that given
any slow or fast inertial particle, all inertial observers agree on the value
of $\mathsf{m}\cdot \sqrt{|1-v^2|}$, where $\mathsf{m}$ is the particle's
relativistic mass and $v$ its speed. This confirms formally the widely held
belief that the relativistic mass and momentum of a positive-mass
faster-than-light particle must decrease as its speed increases.
