  We analyze the Carroll-Field-Jackiw (CFJ) modification of electrodynamics
reformulated as the ordinary Maxwell theory with an additional special axion
field. In this form, the CFJ model appears as a special case of the pre-metric
approach recently developed by Hehl and Obukhov. This embedding turns out to be
non-trivial. Particularly, the pre-metric energy-momentum tensor does not
depend on the axion. This is in contrast to the CFJ energy-momentum tensor
which involves the axion addition explicitly. We show that the relation between
these two quantities is similar to the correspondence between the Noether
conserved tensor and the Hilbert symmetric tensor. As a result the CFJ
energy-momentum tensor appears as the unique conserved closure of the
pre-metric one. Another problem is in the description of the birefringence
effect, which in the pre-metric framework does not depend on the axion. The
comparison with the CFJ model shows that the corresponding wave propagation
(Fresnel) equation has to be extended by a derivative term, which is non zero
for the axion field. In this way, the CFJ birefringence effect is derived in
the metric-free approach. Consequently the Lorentz and CPT violating models can
be embedded without contradictions in the pre-metric approach to
electrodynamics. This correspondence can be useful for both constructions.
