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Reviewer: Edgar R. Chavez

Since it first appeared in 1964, Mendelson's book has been recognized as an excellent textbook in the field. It is one of the most frequently mentioned texts in references and recommended reading lists. The fifth edition has a few additions that add to its value: a new section about nonstandard models of arithmetic; an appendix about modal logic that Mendelson carefully titles "First Steps in Propositional Logic," thereby clearly indicating the level of coverage he intends to present; an expanded and updated bibliography that highlights the ever-widening amount of work in the field; and additional exercises (and selected answers), in which the reader will find ample opportunity to work at different levels of difficulty. Mathematical logic is an area where philosophy, computer science, and mathematics intersect. Mathematical logic is an active, fruitful area of research in all three disciplines. This book is a clear, concise, mathematically rigorous introduction to a large field. Mendelson does an excellent job of meeting the needs of computer scientists and mathematicians. Philosophy students may need to stretch their intellectual muscles to tackle the mathematics in this textbook. For one thing, readers need to be completely comfortable reading and doing mathematical proofs. For those who feel the need for a gentle but thorough introduction to proofs, I recommend Velleman's book [1], which will also help readers acquire a solid acquaintance with the mechanics of predicate logic and quantificational logic. Thompson's excellent review of the third edition of the book [2] does an excellent job of placing the book in the context of computer science and summarizing its contents. I fully agree with his assessment that "this is a first-class textbook in mathematical logic, with much to offer the computer scientist." This book rightfully belongs in the small, elite set of superb books that every computer science graduate, graduate student, scientist, and teacher should be familiar with. Students with adequate background will find Mendelson's book a fecund source of study and enjoyment. The book is also superb for self-study, as readers will welcome the clear style, the attention to precise definitions, the footnotes that highlight and expand concepts that need extra consideration, and the natural progression of theory built on incremental steps from proposition to proposition (propositions are really metatheorems, a concept lucidly explained on page 27). The bibliography is current and extensive. Additionally, Mendelson points out the most helpful references within the text itself, when appropriate. As I have already mentioned, examples and exercises are plentiful and of high quality. Some exercises are meant to fill out details or expand material introduced in the text. Difficult exercises and those that require familiarity with material not fully developed in the text are clearly marked. All readers, but particularly those studying on their own, will be greatly rewarded if they work on all of them. Mendelson includes solutions and hints to a good selection of exercises. The table of contents of the fifth edition can be found on the publisher's Web site [3]. Online Computing Reviews Service