Proton-air collisions in a model of soft interactions at high energies

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.