The chemical evolution of fluorine is investigated in a sample of Milky Way red giant stars that span a significant range in metallicity from [ Fe/H ] \sim -1.3 to 0.0 dex . Fluorine abundances are derived from vibration-rotation lines of HF in high-resolution infrared spectra near \lambda 2.335 \mu m. The red giants are members of the thin and thick disk / halo , with two stars being likely members of the outer disk Monoceros overdensity . At lower metallicities , with [ Fe/H ] < -0.4 to -0.5 , the abundance of F varies as a primary element with respect to the Fe abundance , with a constant subsolar value of [ F/Fe ] \sim -0.3 to -0.4 dex . At larger metallicities , however , [ F/Fe ] increases rapidly with [ Fe/H ] and displays a near-secondary behavior with respect to Fe . Comparisons with various models of chemical evolution suggest that in the low-metallicity regime ( dominated here by thick disk stars ) , a primary evolution of ^ { 19 } F with Fe , with a subsolar [ F/Fe ] value that roughly matches the observed plateau can be reproduced by a model incorporating neutrino nucleosynthesis in the aftermath of the core collapse in supernovae of type II ( SN II ) . A primary behavior for [ F/Fe ] at low metallicity is also observed for a model including rapid rotating low-metallicity massive stars but this overproduces [ F/Fe ] at low metallicity . The thick disk red giants in our sample span a large range of galactocentric distance ( R _ { g } \sim 6–13.7 kpc ) , yet display a \sim constant value of [ F/Fe ] , indicating a very flat gradient ( with a slope of 0.02 \pm 0.03 dex/kpc ) of this elemental ratio over a significant portion of the Galaxy having |Z| > 300 pc away from the Galaxy mid-plane .