  We show that Pomeron interactions generate important corrections to the
Gribov-Glauber formula, which is used to extract proton-proton cross sections
from proton-air collisions at high energy. We show that these corrections are
larger than the errors for proton-air cross sections measured at ultra high
energies in cosmic ray experiments. We present a description of these data in
our model for soft interactions at high energies, which describes all available
accelerator data including that from the LHC.
