  We studied the effects of a hypothetical initial stellar generation (PopIII)
of only massive and very massive stars (VMS) on the chemical evolution of the
Galaxy. We adopted the two-infall chemical evolution model of Chiappini et al.
and tested several sets of yields for primordial VMS (Pair-Creation SNe), which
produce different amounts of heavy elements than lower mass stars. We focused
on the evolution of alpha-elements, C, N, Fe. The effects of PopIII stars on
the Galactic evolution of these elements is negligible if a few generations of
such stars occurred, whereas they produce different results from the standard
models if they formed for a longer period. Also the effects of a more strongly
variable IMF were discussed, making use of suggestions appeared in the
literature to explain the lack of metal-poor stars in the Galactic halo with
respect to model predictions. The predicted variations in abundances, SN rates,
G-dwarf [Fe/H] distribution are here more dramatic and in contrast with
observations; we concluded that a constant or slightly varying IMF is the best
solution. Our main conclusion is that if VMS existed they must have formed only
for a very short period of time (until the halo gas reached the threshold
metallicity for the formation of very massive objects); in this case, their
effects on the evolution of the studied elements was negligible also in the
earliest phases. We thus cannot prove or disprove the existence of such stars
on the basis of the available data. Due to their large metal production and
short lives, primordial VMS should have enriched the halo gas beyond the
metallicity of the most metal poor stars known in a few Myrs. This constrains
the number of Pair-Creation SNe: we find that a number of 2-20 of such SNe
occurred in our Galaxy depending on the stellar yields.
