  The issue of implementing the principle of general relativity in Einstein
equations has been widely discussed, since Kretschmann's well-known criticism
stated that general covariance of the Einstein equations is not suffice to
express the principle of general relativity (the equivalence of all the
coordinate systems). This failure is usually rooted in the fact that metric in
Einstein equations is not univocally determined by the matter distribution. We
show that the condition of univocal determination of the metric by the matter
distribution is stronger than the requirement of equivalence of all coordinate
systems. In order to separate the uniqueness problem in Einstein equations from
the issue of the principle of general relativity, we define the "equivalence
group" instead of the notion of covariance group which is empty of physical
content. Moreover, we have complemented in a positive way Kretschmann's
objection by supplementing Einstein equations with a sufficient condition for
the equivalence of all the coordinate systems.
