  The abundances of iron and oxygen are homogeneously determined in a sample of
523 nearby (d<150 pc) FGK disk and halo stars with metallicities in the range
-1.5<[Fe/H]<0.5. The oxygen abundances were inferred from a restricted non-LTE
analysis of the 777 nm O I triplet. We use the stellar kinematics to compute
the probabilities of our sample stars to be members of the thin disk, thick
disk, or halo of the Galaxy. We find that the majority of the
kinematically-selected thick-disk stars show larger [O/Fe] ratios compared to
thin-disk stars. A close examination of this pattern for disk stars with
ambiguous probabilities shows that an intermediate population with properties
between those of the thin and thick disks does not exist. Excluding the stars
with unusual kinematics, we find that thick-disk stars show slowly decreasing
[O/Fe] ratios from about 0.5 to 0.4 in the -0.8<[Fe/H]<-0.3 range. Using a
simple model for the chemical evolution of the thick disk we show that this
trend results directly from the metallicity dependence of the Type II supernova
yields. At [Fe/H]>-0.3, we find no obvious indication of a sudden decrease
(i.e., a 'knee') in the [O/Fe] vs. [Fe/H] pattern of thick-disk stars that
would connect the thick and thin disk trends at a high metallicity. We conclude
that Type Ia supernovae (SN Ia) did not contribute significantly to the
chemical enrichment of the thick disk. [Abridged]
