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First published in 1990, this book consists of a detailed exposition of results of the theory of "interpretation" developed by G. Kreisel -- the relative impenetrability of which gives the elucidation contained here great value for anyone seeking to understand his work. It contains more complex versions of the information obtained by Kreisel for number theory and clustering around the no-counter-example interpretation, for number-theorectic forumulae provide in ramified analysis. It also proves the omega-consistency of ramified analysis. The author also presents proofs of Sch tte's cut-elimination theorems which are based on his consistency proofs and essentially contain them -- these went further than any published work up to that point, helping to squeeze the maximum amount of information from these proofs.