  Hadronic cross sections at ultra-high energy have a significant impact on the
development of extensive air shower cascades. Therefore the interpretation of
air shower data depends critically on hadronic interaction models that
extrapolate the cross section from accelerator measurements to the highest
cosmic ray energies. We discuss how extreme scenarios of cross section
extrapolations can affect the interpretation of air shower data. We find that
the theoretical uncertainty of the extrapolated proton-air cross section at
ultra-high energies is much larger than suggested by the existing spread of
available Monte Carlo model predictions. The impact on the depth of the shower
maximum is demonstrated.
