  The two closely related Lorentz-invariant partial orders of space-time are
distinguished with respect to the existence of antichain cutsets and the
possibility of grading. World lines of particles with or without mass are the
maximal chains in the causality order of space-time, and antichain cutsets are
the levels of the various gradings of the causality partial order. The maximal
chains of the weaker, subluminal causality order need not be connected
topologically, subluminal causality has no antichain cutsets and cannot be
graded. Combinatorial characterizations of optical lines and hyperplanes,
separation lines, inertia planes and lines, ultimately in terms of the
causality order yield a simple proof of the Alexandrov-Zeeman Theorem.
