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

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