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Computability and Logic
ISBN 0521007585 / 9780521007580 / 0-521-00758-5
Publisher Cambridge University Press
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Now in its fourth edition, this book has become a classic because of its accessibility to students without a mathematical background, and because it covers not only the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has enhanced the book by adding a selection of problems at the end of each chapter. [via]