  The global astrometric observations of a GAIA-like satellite were modeled
within the PPN formulation of Post-Newtonian gravitation. An extensive
experimental campaign based on realistic end-to-end simulations was conducted
to establish the sensitivity of global astrometry to the PPN parameter \gamma,
which measures the amount of space curvature produced by unit rest mass. The
results show that, with just a few thousands of relatively bright,
photometrically stable, and astrometrically well behaved single stars, among
the ~10^9 objects that will be observed by GAIA, \gamma can be estimated after
1 year of continuous observations with an accuracy of ~10^{-5} at the 3\sigma
level. Extrapolation to the full 5-year mission of these results based on the
scaling properties of the adjustment procedure utilized suggests that the
accuracy of \simeq 2x10^{-7}, at the same 3\sigma level, can be reached with
\~10^6 single stars, again chosen as the most astrometrically stable among the
millions available in the magnitude range V=12-13. These accuracies compare
quite favorably with recent findings of scalar-tensor cosmological models,
which predict for \gamma a present-time deviation, |1-\gamma|, from the General
Relativity value between 10^{-5} and 10^{-7}.
