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We present a formalism for high energy soft processes, mediated by Pomerons,which embodies pion-loop insertions in the Pomeron trajectory, rescatteringeffects via a two-channel eikonal and high-mass diffractive dissociation. Itdescribes all the main features of the data throughout the ISR to Tevatronenergy interval. We give predictions for soft diffractive phenomena at the LHCenergy, and we calculate the different survival probabilities of rapidity gapswhich occur in various diffractive processes.Comment: 32 pages, 12 figures, LaTeX; version to be published in EPJC, minor  changes to the text, references and footnote

Soft diffraction and the elastic slope at Tevatron and LHC energies: a multi-Pomeron approach