  Context. The abundances of the three main isotopes of oxygen are altered in
the course of the CNO-cycle. When the first dredge-up mixes the burning
products to the surface, the nucleosynthesis processes can be probed by
measuring oxygen isotopic ratios. Aims. By measuring 16O/17O and 16O/18O in red
giants of known mass we compare the isotope ratios with predictions from
stellar and galactic evolution modelling. Methods. Oxygen isotopic ratios were
derived from the K-band spectra of six red giants. The sample red giants are
open cluster members with known masses of between 1.8 and 4.5 Msun . The
abundance determination employs synthetic spectra calculated with the COMARCS
code. The effect of uncertainties in the nuclear reaction rates, the mixing
length, and of a change in the initial abundance of the oxygen isotopes was
determined by a set of nucleosynthesis and mixing models using the FUNS code.
Results. The observed 16O/17O ratios are in good agreement with the model
results, even if the measured values do not present clear evidence of a
variation with the stellar mass. The observed 16O/18O ratios are clearly lower
than the predictions from our reference model. Variations in nuclear reaction
rates and mixing length parameter both have only a very weak effect on the
predicted values. The 12C/13C ratios of the K giants studied implies the
absence of extra-mixing in these objects. Conclusions. A comparison with
galactic chemical evolution models indicates that the 16O/18O abundance ratio
underwent a faster decrease than predicted. To explain the observed ratios, the
most likely scenario is a higher initial 18O abundance combined with a lower
initial 16 O abundance. Comparing the measured 18 O/17 O ratio with the
corresponding value for the ISM points towards an initial enhancement of 17O as
well. Limitations imposed by the observations prevent this from being a
conclusive result.
