Relativity in space-times with short distance structure governed by an observer independent (Planckian) length scale

I show that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of spacetimes whose short-distance structure is governed by an observer-independent length scale. The consistency of these postulates proves incorrect the expectation that modifications of the rules of kinematics involving the Planck length would necessarily require the introduction of a preferred class of inertial observers. In particular, it is possible for every inertial observer to agree on physical laws supporting deformed dispersion relations of the type E2-c2 p2-c4m2 + f(E, p, m; Lp) =0, at least for certain types of f.