  We study the relationship between age, metallicity, and alpha-enhancement of
FGK stars in the Galactic disk. The results are based upon the analysis of
high-resolution UVES spectra from the Gaia-ESO large stellar survey. We explore
the limitations of the observed dataset, i.e. the accuracy of stellar
parameters and the selection effects that are caused by the photometric target
preselection. We find that the colour and magnitude cuts in the survey suppress
old metal-rich stars and young metal-poor stars. This suppression may be as
high as 97% in some regions of the age-metallicity relationship. The dataset
consists of 144 stars with a wide range of ages from 0.5 Gyr to 13.5 Gyr,
Galactocentric distances from 6 kpc to 9.5 kpc, and vertical distances from the
plane 0 < |Z| < 1.5 kpc. On this basis, we find that i) the observed
age-metallicity relation is nearly flat in the range of ages between 0 Gyr and
8 Gyr; ii) at ages older than 9 Gyr, we see a decrease in [Fe/H] and a clear
absence of metal-rich stars; this cannot be explained by the survey selection
functions; iii) there is a significant scatter of [Fe/H] at any age; and iv)
[Mg/Fe] increases with age, but the dispersion of [Mg/Fe] at ages > 9 Gyr is
not as small as advocated by some other studies. In agreement with earlier
work, we find that radial abundance gradients change as a function of vertical
distance from the plane. The [Mg/Fe] gradient steepens and becomes negative. In
addition, we show that the inner disk is not only more alpha-rich compared to
the outer disk, but also older, as traced independently by the ages and Mg
abundances of stars.
