A textbook for a one-year graduate course for students familiar with the simplest properties of natural numbers, real numbers, and sets and a slight acquaintance with modern algebra, though some of the problems require more advanced learning. Shoenfield (deceased; formely affiliated with Duke U.) focuses on the central theories of proofs, models, recursion, axiomatic numbers, and sets. There is no bibliography. Addison-Wesley published the original as part of a series on logic. Annotation c. Book News, Inc., Portland, OR (booknews.com)