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Basic Proof Theory
 Anne S. Troelstra
 This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of firstorder logic. Examples are given of several areas of application, namely: the metamathematics of pure firstorder logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; firstorder arithmetic and secondorder logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in firstorder logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.



