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We study the relationship between age, metallicity, and α-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 kpcto 9.5 kpc, and vertical distances from the plane 0 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 α-rich compared to the outer disk, but also older, as traced independently by the ages and Mg abundances of stars. ; This work was partly supported by the European Union FP7 programme through ERC grant number 320360. AS is supported by the MICINN grant AYA2011-24704 and by the ESF EUROCORES Programme EuroGENESIS (MICINN grant EUI2009-04170). The results presented here benefited from discussions held during Gaia-ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT (Gaia Research ...